UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM N-Q

       QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
                               INVESTMENT COMPANY

                  Investment Company Act file number 811-22528
                                                    -----------

                     First Trust Energy Infrastructure Fund
           ---------------------------------------------------------
               (Exact name of registrant as specified in charter)

                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
           ---------------------------------------------------------
              (Address of principal executive offices) (Zip code)

                             W. Scott Jardine, Esq.

                          First Trust Portfolios L.P.
                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
           ---------------------------------------------------------
                    (Name and address of agent for service)

        Registrant's telephone number, including area code: 630-765-8000
                                                           --------------

                      Date of fiscal year end: November 30
                                              -------------

                   Date of reporting period:  August 31, 2017
                                            -------------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q unless the
Form displays a currently valid Office of Management and Budget ("OMB") control
number. Please direct comments concerning the accuracy of the information
collection burden estimate and any suggestions for reducing the burden to the
Secretary, Securities and Exchange Commission, 100 F Street, NE, Washington, DC
20549. The OMB has reviewed this collection of information under the clearance
requirements of 44 U.S.C. ss. 3507.





ITEM 1. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.


FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (a)
AUGUST 31, 2017 (UNAUDITED)



    SHARES                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
COMMON STOCKS - 94.0%

                                                                                 
                 ELECTRIC UTILITIES - 25.0%
         90,900  Alliant Energy Corp.................................................  $    3,885,066
          9,500  American Electric Power Co., Inc....................................         699,485
        104,500  Duke Energy Corp....................................................       9,122,850
         15,900  Edison International................................................       1,274,862
        247,900  Emera, Inc. (CAD)...................................................       9,520,948
        155,000  Eversource Energy...................................................       9,765,000
        257,200  Exelon Corp.........................................................       9,740,164
        165,400  Fortis, Inc. (CAD)..................................................       6,051,752
        188,300  Hydro One Ltd. (CAD) (b)............................................       3,493,823
         64,000  IDACORP, Inc........................................................       5,694,720
         66,900  NextEra Energy, Inc.................................................      10,069,119
        189,300  Southern (The) Co...................................................       9,135,618
        123,400  Xcel Energy, Inc....................................................       6,108,300
                                                                                       --------------
                                                                                           84,561,707
                                                                                       --------------

                 GAS UTILITIES - 6.3%
         45,600  Atmos Energy Corp...................................................       4,014,624
         60,310  Chesapeake Utilities Corp...........................................       4,791,630
        110,500  New Jersey Resources Corp...........................................       4,823,325
        150,018  UGI Corp............................................................       7,412,389
                                                                                       --------------
                                                                                           21,041,968
                                                                                       --------------

                 MULTI-UTILITIES - 18.1%
        127,200  ATCO, Ltd., Class I (CAD)...........................................       4,686,664
        211,700  Canadian Utilities Ltd., Class A (CAD)..............................       6,598,089
        142,800  CMS Energy Corp.....................................................       6,931,512
        157,592  National Grid PLC, ADR..............................................      10,059,098
        179,800  NiSource, Inc.......................................................       4,831,226
        257,000  Public Service Enterprise Group, Inc................................      12,037,880
          4,100  SCANA Corp..........................................................         247,558
         73,900  Sempra Energy.......................................................       8,715,027
        107,700  WEC Energy Group, Inc...............................................       7,024,194
                                                                                       --------------
                                                                                           61,131,248
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 44.2%
      2,203,750  Enbridge Energy Management, LLC (c).................................      31,756,037
        625,200  Enbridge Income Fund Holdings, Inc. (CAD)...........................      15,505,461
        232,400  Enbridge, Inc.......................................................       9,293,676
        325,700  Inter Pipeline, Ltd. (CAD)..........................................       5,964,972
        172,100  Keyera Corp. (CAD)..................................................       4,994,518
        606,175  Kinder Morgan, Inc..................................................      11,717,363
        223,053  ONEOK, Inc..........................................................      12,080,550
        764,100  Plains GP Holdings, L.P.............................................      17,176,968
         15,600  Targa Resources Corp................................................         695,292
        423,170  TransCanada Corp....................................................      21,497,036
        632,600  Williams (The) Cos., Inc............................................      18,807,198
                                                                                       --------------
                                                                                          149,489,071
                                                                                       --------------



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (a) (CONTINUED)
AUGUST 31, 2017 (UNAUDITED)



    SHARES/
     UNITS                                   DESCRIPTION                                   VALUE
---------------  --------------------------------------------------------------------  --------------
COMMON STOCKS (CONTINUED)

                                                                                 
                 WATER UTILITIES - 0.4%
         15,900  American Water Works Co., Inc.......................................  $    1,286,310
                                                                                       --------------
                 TOTAL COMMON STOCKS.................................................     317,510,304
                 (Cost $312,905,897)                                                   --------------

MASTER LIMITED PARTNERSHIPS - 35.7%

                 CHEMICALS - 0.2%
         22,000  Westlake Chemical Partners, L.P.....................................         526,900
                                                                                       --------------

                 GAS UTILITIES - 1.6%
        122,152  AmeriGas Partners, L.P..............................................       5,300,175
                                                                                       --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 5.0%
        410,555  NextEra Energy Partners, L.P. (d)...................................      17,021,611
                                                                                       --------------

                 OIL, GAS & CONSUMABLE FUELS - 28.9%
         79,700  Alliance Holdings GP, L.P...........................................       2,195,735
        306,330  Alliance Resource Partners, L.P.....................................       5,789,637
         65,700  Buckeye Partners, L.P...............................................       3,757,383
          7,600  Dominion Energy Midstream Partners, L.P.............................         217,740
        757,700  Enterprise Products Partners, L.P...................................      19,753,239
        176,100  EQT Midstream Partners, L.P.........................................      13,448,757
        266,976  Holly Energy Partners, L.P..........................................       8,714,097
        100,300  Magellan Midstream Partners, L.P....................................       6,759,217
        121,472  NGL Energy Partners, L.P............................................       1,087,174
        103,600  Phillips 66 Partners, L.P...........................................       4,950,008
         65,000  Plains All American Pipeline, L.P...................................       1,407,900
         41,000  Shell Midstream Partners, L.P.......................................       1,134,470
        280,300  Spectra Energy Partners, L.P........................................      12,425,699
         47,328  Tallgrass Energy Partners, L.P......................................       2,237,195
        161,495  TC PipeLines, L.P...................................................       8,497,867
         56,002  TransMontaigne Partners, L.P........................................       2,534,650
         75,000  Williams Partners, L.P..............................................       2,955,000
                                                                                       --------------
                                                                                           97,865,768
                                                                                       --------------
                 TOTAL MASTER LIMITED PARTNERSHIPS...................................     120,714,454
                 (Cost $101,471,778)                                                   --------------

REAL ESTATE INVESTMENT TRUSTS - 1.4%

                 EQUITY REAL ESTATE INVESTMENT TRUSTS - 1.4%
         49,101  CorEnergy Infrastructure Trust, Inc.................................       1,602,166
        142,050  InfraREIT, Inc......................................................       3,194,704
                                                                                       --------------
                 TOTAL REAL ESTATE INVESTMENT TRUSTS.................................       4,796,870
                 (Cost $4,641,045)                                                     --------------

                 TOTAL INVESTMENTS - 131.1%..........................................     443,021,628
                 (Cost $419,018,720) (e)                                               --------------



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (a) (CONTINUED)
AUGUST 31, 2017 (UNAUDITED)



   NUMBER OF                                              NOTIONAL        EXERCISE       EXPIRATION
   CONTRACTS                 DESCRIPTION                   AMOUNT          PRICE            DATE           VALUE
---------------  ------------------------------------  --------------  --------------  --------------  --------------
CALL OPTIONS WRITTEN - (0.7%)

                                                                                        
            600  Buckeye Partners, L.P. .............  $   3,431,400   $    60.00         Jan 2018     $      (66,000)
            800  CMS Energy Corp. (f) ...............      3,883,200        50.00         Sep.2017             (4,000)
            700  Enbridge, Inc. .....................      2,799,300        42.50         Jan 2018            (50,750)
          1,600  Enbridge, Inc. .....................      6,398,400        45.00         Jan 2018            (36,000)
            500  Enterprise Products Partners, L.P.
                    (f) .............................      1,303,500        28.00         Sep.2017             (1,000)
          6,400  Enterprise Products Partners, L.P...     16,684,800        29.00         Dec 2017            (80,000)
            600  Enterprise Products Partners, L.P...      1,564,200        27.00         Jan 2018            (39,000)
            600  Exelon Corp. .......................      2,272,200        39.00         Sep 2017             (6,000)
            900  Exelon Corp. .......................      3,408,300        38.00         Oct 2017            (81,000)
            900  Exelon Corp. .......................      3,408,300        39.00         Oct 2017            (40,500)
            100  Exelon Corp. .......................        378,700        40.00         Oct 2017             (1,500)
          1,300  Kinder Morgan, Inc. ................      2,512,900        20.00         Sep 2017            (11,700)
          4,700  Kinder Morgan, Inc. ................      9,085,100        21.00         Sep 2017             (9,400)
            600  Magellan Midstream Partners, L.P....      4,043,400        72.50         Sep 2017             (3,000)
            200  Magellan Midstream Partners, L.P....      1,347,800        70.00         Oct 2017            (10,000)
            200  Magellan Midstream Partners, L.P....      1,347,800        72.50         Oct 2017             (3,000)
          1,500  National Grid PLC ..................      9,574,500        65.00         Dec 2017           (202,500)
            100  NextEra Energy, Inc. ...............      1,505,100       150.00         Sep 2017            (19,500)
          1,000  NiSource, Inc. .....................      2,687,000        27.00         Oct 2017            (52,500)
            700  NiSource, Inc. .....................      1,880,900        28.00         Oct 2017            (10,500)
            700  ONEOK, Inc. ........................      3,791,200        52.50         Oct 2017           (199,500)
          1,500  ONEOK, Inc. ........................      8,124,000        55.00         Oct 2017           (210,000)
            600  Plains All American Pipeline, L.P...      1,299,600        23.00         Nov 2017            (36,000)
          2,500  Public Service Enterprise Group,
                    Inc. ............................     11,710,000        45.00         Dec 2017           (595,000)
            600  Sempra Energy ......................      7,075,800       125.00         Jan 2018            (64,500)
            200  Southern (The) Co. .................        965,200        50.00         Oct 2017             (5,000)
          1,600  Southern (The) Co. .................      7,721,600        49.00         Nov 2017           (124,800)
            100  Targa Resources Corp. ..............        445,700        50.00         Oct 2017             (1,500)
            800  TransCanada Corp. ..................      4,064,000        50.00         Nov 2017           (112,000)
            400  WEC Energy Group, Inc. .............      2,608,800        65.00         Oct 2017            (53,200)
          1,500  Williams (The) Cos., Inc. ..........      4,459,500        30.00         Sep 2017            (36,000)
          2,100  Williams (The) Cos., Inc. (f).......      6,243,300        33.00         Sep.2017             (4,200)
          2,700  Williams (The) Cos., Inc. ..........      8,027,100        31.00         Nov 2017           (148,500)
            600  Williams Partners, L.P. ............      2,364,000        40.00         Sep 2017            (21,000)
                                                                                                       --------------
                 TOTAL CALL OPTIONS WRITTEN..........................................................      (2,339,050)
                 (Premiums received $2,163,155)                                                        --------------

                 OUTSTANDING LOAN - (33.6%)..........................................................    (113,500,000)

                 NET OTHER ASSETS AND LIABILITIES - 3.2%.............................................      10,842,251
                                                                                                       --------------
                 NET ASSETS - 100.0%.................................................................  $  338,024,829
                                                                                                       ==============



                        See Notes to Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2017 (UNAUDITED)


-----------------------------

INTEREST RATE SWAP AGREEMENTS:


                        FLOATING      EXPIRATION      NOTIONAL       FIXED
   COUNTERPARTY         RATE (1)         DATE          AMOUNT       RATE (1)       VALUE
---------------------------------------------------------------------------------------------
                                                                
Bank of Nova Scotia   1 month LIBOR    10/08/20    $   36,475,000    2.121%    $     (714,076)
Bank of Nova Scotia   1 month LIBOR    09/03/24        36,475,000    2.367%        (1,432,680)
                                                   --------------              --------------
                                                   $   72,950,000              $   (2,146,756)
                                                   ==============              ==============


(1)   The Fund pays the fixed rate and receives the floating rate. The floating
      rate on August 31, 2017 was 1.229% and 1.232%, respectively.

-----------------------------

(a)   All of these securities are available to serve as collateral for the
      outstanding loans.

(b)   This security is restricted in the U.S. and cannot be offered for public
      sale without first being registered under the Securities Act of 1933, as
      amended. This security is not restricted on the foreign exchange where it
      trades freely without any additional registration. As such, it does not
      require the additional disclosure required of restricted securities.


(c)   Non-income producing security that makes payment-in-kind ("PIK")
      distributions. For the fiscal year-to-date period (December 1, 2016
      through August 31, 2017), the Fund received 137,069 PIK shares of Enbridge
      Energy Management, LLC.

(d)   NextEra Energy Partners, L.P. is taxed as a "C" corporation for federal
      income tax purposes.

(e)   Aggregate cost for financial reporting purposes approximates the aggregate
      cost for federal income tax purposes. As of August 31, 2017, the aggregate
      gross unrealized appreciation for all investments in which there was an
      excess of value over tax cost was $48,111,257 and the aggregate gross
      unrealized depreciation for all investments in which there was an excess
      of tax cost over value was $26,431,000. The net unrealized appreciation
      was $21,680,257. The amounts presented are inclusive of derivative
      contracts.

(f)   This security is fair valued by First Trust Advisors L.P.'s Pricing
      Committee in accordance with procedures adopted by the Fund's Board of
      Trustees, and in accordance with the provisions of the Investment Company
      Act of 1940, as amended. At August 31, 2017, securities noted as such are
      valued at $(9,200) or (0.0)% of net assets.

ADR   American Depositary Receipt

CAD   Canadian Dollar - Security is denominated in Canadian Dollars and is
      translated into U.S. Dollars based upon the current exchange rate.

-----------------------------

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of August 31,
2017 is as follows (see Note 2A - Portfolio Valuation in the Notes to Portfolio
of Investments):



                                                    ASSETS TABLE

                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   8/31/2017          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
                                                                                          
Common Stocks*................................  $   317,510,304   $   317,510,304   $            --   $            --
Master Limited Partnerships*..................      120,714,454       120,714,454                --                --
Real Estate Investment Trusts*................        4,796,870         4,796,870                --                --
                                                ---------------   ---------------   ---------------   ---------------
Total Investments.............................  $   443,021,628   $   443,021,628   $            --   $            --
                                                ===============   ===============   ===============   ===============


                                                  LIABILITIES TABLE
                                                                                        LEVEL 2           LEVEL 3
                                                     TOTAL            LEVEL 1         SIGNIFICANT       SIGNIFICANT
                                                   VALUE AT           QUOTED          OBSERVABLE       UNOBSERVABLE
                                                   8/31/2017          PRICES            INPUTS            INPUTS
                                                ---------------   ---------------   ---------------   ---------------
Call Options Written..........................  $    (2,339,050)  $    (1,830,100)  $      (508,950)  $            --
Interest Rate Swaps**.........................       (2,146,756)               --        (2,146,756)               --
                                                ---------------   ---------------   ---------------   ---------------
                                                $    (4,485,806)  $    (1,830,100)  $    (2,655,706)  $            --
                                                ===============   ===============   ===============   ===============



*   See Portfolio of Investments for industry breakout.
**  See Interest Rate Swap Agreements for contract detail.

All transfers in and out of the Levels during the period are assumed to occur on
the last day of the period at their current value. There were no transfers
between Levels at August 31, 2017.


                        See Notes to Portfolio of Investments





NOTES TO PORTFOLIO OF INVESTMENTS

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2017 (UNAUDITED)


                                1. ORGANIZATION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011 and is registered with the Securities and Exchange
Commission (the "SEC") under the Investment Company Act of 1940, as amended (the
"1940 Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").

The Fund is considered an investment company and follows accounting and
reporting guidance under Financial Accounting Standards Board Accounting
Standards Codification Topic 946, "Financial Services-Investment Companies."

                       2. SIGNIFICANT ACCOUNTING POLICIES

A. PORTFOLIO VALUATION

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. Foreign securities are
priced using data reflecting the earlier closing of the principal markets for
those securities. The Fund's NAV per Common Share is calculated by dividing the
value of all assets of the Fund (including accrued interest and dividends), less
all liabilities (including accrued expenses, dividends declared but unpaid and
any borrowings of the Fund) by the total number of Common Shares outstanding.

The Fund's investments are valued daily at market value or, in the absence of
market value with respect to any portfolio securities, at fair value. Market
value prices represent last sale or official closing prices from a national or
foreign exchange (i.e., a regulated market) and are primarily obtained from
third-party pricing services. Fair value prices represent any prices not
considered market value prices and are either obtained from a third-party
pricing service or are determined by the Pricing Committee of the Fund's
investment advisor, First Trust Advisors L.P. ("First Trust" or the "Advisor"),
in accordance with valuation procedures adopted by the Fund's Board of Trustees,
and in accordance with provisions of the 1940 Act. Investments valued by the
Advisor's Pricing Committee, if any, are footnoted as such in the footnotes to
the Portfolio of Investments. The Fund's investments are valued as follows:

      Common stocks, master limited partnerships ("MLPs"), real estate
      investment trusts ("REITs"), and other equity securities listed on any
      national or foreign exchange (excluding The Nasdaq Stock Market LLC
      ("Nasdaq") and the London Stock Exchange Alternative Investment Market
      ("AIM")) are valued at the last sale price on the exchange on which they
      are principally traded, or for Nasdaq and AIM securities, the official
      closing price. Securities traded on more than one securities exchange are
      valued at the last sale price or official closing price, as applicable, at
      the close of the securities exchange representing the principal market for
      such securities.

      Exchange-traded options contracts are valued at the closing price in the
      market where such contracts are principally traded. If no closing price is
      available, exchange-traded options contracts are fair valued at the mean
      of their most recent bid and asked price, if available, and otherwise at
      their closing bid price. Over-the-counter options contracts are fair
      valued at the mean of their most recent bid and asked price, if available,
      and otherwise their closing bid price.

      Securities traded in an over-the-counter market are fair valued at the
      mean of their most recent bid and asked price, if available, and otherwise
      at their closing bid price.

      Swaps are fair valued utilizing quotations provided by a third-party
      pricing service or, if the pricing service does not provide a value, by
      quotes provided by the selling dealer or financial institution.

Certain securities may not be able to be priced by pre-established pricing
methods. Such securities may be valued by the Fund's Board of Trustees or its
delegate, the Advisor's Pricing Committee, at fair value. These securities
generally include, but are not limited to, restricted securities (securities
which may not be publicly sold without registration under the Securities Act of
1933, as amended (the "1933 Act")) for which a third-party pricing service is
unable to provide a market price; securities whose trading has been formally
suspended; a security whose market or fair value price is not available from a
pre-established pricing source; a security with respect to which an event has
occurred that is likely to materially affect the value of the security after the
market has closed but before the calculation of the Fund's NAV or make it
difficult or impossible to obtain a reliable market quotation; and a security
whose price, as provided by the third-party pricing service, does not reflect
the security's fair value. As a general principle, the current fair value of a
security would appear to be the amount which the owner might reasonably expect
to receive for the security upon its current sale. When fair value prices are
used, generally they will differ from market quotations or official closing
prices on the applicable exchanges. A variety of factors may be considered in
determining the fair value of such securities, including, but not limited to,
the following:

      1)    the type of security;

      2)    the size of the holding;

      3)    the initial cost of the security;

      4)    transactions in comparable securities;





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2017 (UNAUDITED)


      5)    price quotes from dealers and/or third-party pricing services;

      6)    relationships among various securities;

      7)    information obtained by contacting the issuer, analysts, or the
            appropriate stock exchange;

      8)    an analysis of the issuer's financial statements; and

      9)    the existence of merger proposals or tender offers that might affect
            the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

      1)    the value of similar foreign securities traded on other foreign
            markets;

      2)    ADR trading of similar securities;

      3)    closed-end fund trading of similar securities;

      4)    foreign currency exchange activity;

      5)    the trading prices of financial products that are tied to baskets of
            foreign securities;

      6)    factors relating to the event that precipitated the pricing problem;

      7)    whether the event is likely to recur; and

      8)    whether the effects of the event are isolated or whether they affect
            entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

      o     Level 1 - Level 1 inputs are quoted prices in active markets for
            identical investments. An active market is a market in which
            transactions for the investment occur with sufficient frequency and
            volume to provide pricing information on an ongoing basis.

      o     Level 2 - Level 2 inputs are observable inputs, either directly or
            indirectly, and include the following:

            o     Quoted prices for similar investments in active markets.

            o     Quoted prices for identical or similar investments in markets
                  that are non-active. A non-active market is a market where
                  there are few transactions for the investment, the prices are
                  not current, or price quotations vary substantially either
                  over time or among market makers, or in which little
                  information is released publicly.

            o     Inputs other than quoted prices that are observable for the
                  investment (for example, interest rates and yield curves
                  observable at commonly quoted intervals, volatilities,
                  prepayment speeds, loss severities, credit risks, and default
                  rates).

            o     Inputs that are derived principally from or corroborated by
                  observable market data by correlation or other means.

      o     Level 3 - Level 3 inputs are unobservable inputs. Unobservable
            inputs may reflect the reporting entity's own assumptions about the
            assumptions that market participants would use in pricing the
            investment.

The inputs or methodologies used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of August 31, 2017, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock and MLPs held in the Fund's portfolio as determined to be
appropriate by Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"). The
number of options the Fund can write (sell) is limited by the amount of common
stock and MLPs the Fund holds in its portfolio. The Fund will not write (sell)
"naked" or uncovered options. Options are marked-to-market daily and their value
will be affected by changes in the value and dividend rates of the underlying
equity securities, changes in interest rates, changes in the actual or perceived
volatility of the securities markets and the underlying equity securities and
the remaining time to the options' expiration. The value of options may also be
adversely affected if the market for the options becomes less liquid or trading
volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss. If the price
of the underlying equity security is less than the option's strike price, the
option will likely expire without being exercised. The option premium received
by the Fund will, in this case, be treated as short-term capital gain on the
expiration date of the option. The Fund may also elect to close out its position
in an option prior to its expiration by purchasing an option of the same series
as the option written (sold) by the Fund.





NOTES TO PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2017 (UNAUDITED)


The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at
inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security
covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Over-the-counter options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SWAP AGREEMENTS

The Fund may enter into total return equity swap and interest rate swap
agreements. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed upon prices, rates,
etc. Swap agreements are individually negotiated and involve the risk of the
potential inability of the Counterparties to meet the terms of the agreement. In
connection with these agreements, cash and securities may be identified as
collateral in accordance with the terms of the respective swap agreements to
provide assets of value and recourse in the event of default under the swap
agreement or bankruptcy/insolvency of a party to the swap agreement. In the
event of a default by a Counterparty, the Fund will seek withdrawal of the
collateral and may incur certain costs exercising its rights with respect to the
collateral. If a Counterparty becomes bankrupt or otherwise fails to perform its
obligations due to financial difficulties, the Fund may experience significant
delays in obtaining any recovery in a bankruptcy or other reorganization
proceeding. The Fund may obtain only limited recovery or may obtain no recovery
in such circumstances.

Swap agreements may increase or decrease the overall volatility of the
investments of the Fund. The performance of swap agreements may be affected by
changes in the specific interest rate, security, currency, or other factors that
determine the amounts of payments due to and from the Fund. The Fund's maximum
equity price risk to meet its future payments under swap agreements outstanding
at August 31, 2017 is equal to the total notional amount as shown on the
Portfolio of Investments. The notional amount represents the U.S. dollar value
of the contract as of the day of the opening transaction or contract reset.

The Fund held interest rate swap agreements at August 31, 2017 to hedge against
changes in borrowing rates under the Fund's committed facility agreement. An
interest rate swap agreement involves the Fund's agreement to exchange a stream
of interest payments for another party's stream of cash flows. Interest rate
swaps do not involve the delivery of securities or other underlying assets or
principal. Accordingly, the risk of loss with respect to interest rate swaps is
limited to the net amount of interest payments that the Fund is contractually
obligated to make.

D. SECURITIES TRANSACTIONS AND INVESTMENT INCOME

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.

E. FOREIGN CURRENCY

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investments and items of income and expense are
translated on the respective dates of such transactions.

                           3. DERIVATIVE TRANSACTIONS

During the fiscal period ended August 31, 2017, the premiums for written options
opened were $6,361,015, and the premiums for written options closed, exercised
and expired were $5,565,045.

The average volume of interest rate swaps was $72,950,000 for the fiscal
year-to-date period (December 1, 2016 through August 31, 2017).





ITEM 2. CONTROLS AND PROCEDURES.

(a)   The registrant's principal executive and principal financial officers, or
      persons performing similar functions, have concluded that the registrant's
      disclosure controls and procedures (as defined in Rule 30a-3(c) under the
      Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR
      270.30a-3(c))) are effective, as of a date within 90 days of the filing
      date of the report that includes the disclosure required by this
      paragraph, based on their evaluation of these controls and procedures
      required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and
      Rules 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934, as
      amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b)   There were no changes in the registrant's internal control over financial
      reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
      270.30a-3(d)) that occurred during the registrant's last fiscal quarter
      that have materially affected, or are reasonably likely to materially
      affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section 302 of
the Sarbanes-Oxley Act of 2002 are attached hereto.





                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)        First Trust Energy Infrastructure Fund
              ---------------------------------------------------

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 19, 2017
     ------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 19, 2017
     ------------------

By (Signature and Title)*               /s/ Donald P. Swade
                                        ----------------------------------------
                                        Donald P. Swade
                                        Treasurer, Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)

Date: October 19, 2017
     ------------------

*Print the name and title of each signing officer under his or her signature.