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

                                  SCHEDULE 13G


                   Under the Securities Exchange Act of 1934

                             (Amendment No. ____)*


                      Nuveen Premium Income Municipal Fund, Inc.
                   ------------------------------------------------
                                (Name of Issuer)


                                     Common
                         ------------------------------
                         (Title of Class of Securities)


                                    67062T100
                                 --------------
                                 (CUSIP Number)


                               December 31, 2012
            -------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this
Schedule is filed:

          [ X ]     Rule 13d-1(b)

          [   ]     Rule 13d-1(c)

          [   ]     Rule 13d-1(d)


*The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class
of securities, and for any subsequent amendment containing information
which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities
Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of
that section of the Act but shall be subject to all other provisions of
the Act (however, see the Notes).


                                     - 1 -


CUSIP No. 67062T100

                1.  Names of Reporting Persons, I.R.S. Identification Nos.
                    of above persons (entities only):

                    First Trust Portfolios L.P.: 36-3768815

                    First Trust Advisors L.P.:   36-3788904

                    The Charger Corporation:     36-3772451


                2.  Check the Appropriate Box if a Member of a Group
                    (See Instructions)

                    (a)  [   ]

                    (b)  [   ]


                3.  SEC Use Only


                4.  Citizenship or Place of Organization of each

                    Reporting Person:     Illinois, U.S.A.


Number of       5.  Sole Voting Power:    0
Shares Bene-
ficially
Owned by Each   6.  Shared Voting Power:
Reporting           Such shares are held by the following entities in the
Person With:        respective amounts listed:

                    First Trust Portfolios L.P.: 0

                    First Trust Advisors L.P.:   60,680

                    The Charger Corporation:     60,680


                7.  Sole Dispositive Power:      0

                8.  Shared Dispositive Power:

                    Such shares are held by the following entities in the
                    respective amounts listed:

                    First Trust Portfolios L.P.: 3,661,573

                    First Trust Advisors L.P.:   3,722,253

                    The Charger Corporation:     3,722,253



                9.  Aggregate Amount Beneficially Owned by Each
                    Reporting Person: 3,722,253


               10.  Check if the Aggregate Amount in Row (9) Excludes
                    Certain Shares (See Instructions)


                                     - 2 -


               11.  Percent of Class Represented by Amount in Row (9): 5.82%


               12.  Type of Reporting Person (See Instructions)

                         First Trust Portfolios L.P.      - BD

                         First Trust Advisors L.P.        - IA

                         The Charger Corporation          - HC


ITEM 1.

          (a)       Name of Issuer: Nuveen Premium Income Municipal Fund, Inc.

          (b)       Address of issuer's Principal Executive Offices

                         Attn: Legal Department
                         333 West Wacker Drive
                         Chicago, IL 60606
                         USA



ITEM 2.

          (a)       Name of Person Filing

                         First Trust Portfolios L.P.
                         First Trust Advisors L.P.
                         The Charger Corporation


          (b)       Address of Principal Business Office or, if none, Residence

                         First Trust Portfolios L.P.
                         120 East Liberty Drive, Suite 400
                         Wheaton, Illinois 60187

                         First Trust Advisors L.P.
                         120 East Liberty Drive, Suite 400
                         Wheaton, Illinois 60187

                         The Charger Corporation
                         120 East Liberty Drive, Suite 400
                         Wheaton, Illinois 60187


          (c)       Citizenship of each Reporting Person:

                    Illinois, U.S.A.


          (d)       Title of Class of Securities

                    Common Stock


          (e)       CUSIP Number  67062T100


                                     - 3 -



ITEM 3.   If this statement is filed pursuant to Sec. 240.13d-1(b) or
          240.13d-2(b) or (c), check whether the person filing is a:

          (a)   x   Broker or dealer registered under section 15 of the Act
                    (15 U.S.C. 78o).

          (b)       Bank as defined in section 3(a)(6) of the Act
                    (15 U.S.C. 78c).

          (c)       Insurance company as defined in section 3(a)(19) of the Act
                    (15 U.S.C. 78c).

          (d)       Investment company registered under section 8 of the
                    Investment Company Act of 1940 (15 U.S.C. 80a-8).

          (e)   x   An investment adviser in accordance with
                    Sec. 240.13d-1 (b)(1)(ii)(E).

          (f)       An employee benefit plant or endowment fund in accordance
                    with Sec. 140.13d-1(b)(1)(ii)(F).

          (g)   x   A parent holding company or control person in accordance
                    with Sec. 240.13d-1(b)(1)(ii)(G).

          (h)       A savings associations as defined in Section 3(b) of the
                    Federal Deposit Insurance Act (12 U.S.C. 1813).

          (i)       A church plan that is excluded from the definition of an
                    investment company under section 3(c)(14) of the Investment
                    Company Act of 1940 (15 U.S.C. 80a-3).

          (j)       Group, in accordance with Sec. 240.13d-1(b)1(ii)(J).


ITEM 4.   Ownership

          Provide the following information regarding the aggregate number and
          percentage of the class of securities of the issuer identified in
          Item 1.

          (a)   Amount beneficially owned:  3,722,253

          (b)   Percent of class:           5.82%

          (c)   Number of shares as to which the person has:

                    (i)   Sole power to vote or to direct the vote:     0

                   (ii)   Shared power to vote or to direct the vote:   60,680

                  (iii)   Sole power to dispose or to direct the disposition

                          of:  0

                   (iv)   Shared power to dispose or to direct the disposition

                          of:  3,722,253


                                     - 4 -


Instruction.  For computations regarding securities which represent a right to
              acquire an underlying security see Sec. 204.13d-3(d)(1).

ITEM 5.   Ownership of Five Percent or Less of a Class

          If this statement is being filed to report the fact that as of the
          date hereof the reporting person has ceased to be the beneficial owner
          of more than five percent of the class of securities, check the
          following [   ].



Instruction:  Dissolution of a group requires a response to this item.

ITEM 6.   Ownership of More than Five Percent on Behalf of Another Person

This Schedule 13G filing is jointly filed by The Charger Corporation, First
Trust Portfolios L.P. and First Trust Advisors L.P. pursuant to Rule
13d-1(k)(1). The Charger Corporation is the General Partner of both First Trust
Portfolios L.P. and First Trust Advisors L.P. First Trust Portfolios L.P. acts
as sponsor of certain unit investment trusts which hold shares of the issuer.
The total number of shares of the issuer held by these unit investment trusts
is set forth in Row (8) above with respect to First Trust Portfolios L.P. No
individual unit investment trust sponsored by First Trust Portfolios L.P. holds
more than 3% of any registered investment company issuer's shares. First Trust
Advisors L.P., an affiliate of First Trust Portfolios L.P., acts as portfolio
supervisor of the unit investment trusts sponsored by First Trust Portfolios
L.P., certain of which hold shares of the issuer. Neither First Trust Portfolios
L.P., First Trust Advisors L.P. nor The Charger Corporation have the power to
vote the shares of the issuer held by these unit investment trusts sponsored by
First Trust Portfolios L.P. These shares are voted by the trustee of such unit
investment trusts so as to insure that the shares are voted as closely as
possible in the same manner and in the same general proportion as are the shares
held by owners other than such unit investment trusts. The difference, if any,
between the aggregate amount of shares beneficially owned by each reporting
person, as set forth in Row (9) above, and the number of shares of the issuer
held by the unit investment trusts sponsored by First Trust Portfolios L.P.
represents shares of the issuer which are either held in other registered
investment companies, pooled investment vehicles and/or separately managed
accounts for which First Trust Advisors L.P. serves as investment advisor and/or
investment sub-advisor. Each of First Trust Portfolios L.P., First Trust
Advisors L.P. and The Charger Corporation disclaims beneficial ownership of the
shares of the issuer identified in this filing.



ITEM 7.   Identification and Classification of the Subsidiary Which Acquired
          the Security Being Reported on By the Parent Holding Company

          See Item 6.



ITEM 8.   Identification and Classification of Members of the Group

          Not Applicable.



                                     - 5 -



ITEM 9.   Notice of Dissolution of Group

          Not Applicable.



ITEM 10.  Certification

     By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were acquired and are held in the
ordinary course of business and were not acquired and are not held for
the purpose of or with the effect of changing or influencing the control
of the issuer of the securities and were not acquired and are not held
in connection with or as a participant in any transaction having that
purpose or effect.



                                   SIGNATURE

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete
and correct.

                                  FIRST TRUST PORTFOLIOS L.P.,
                                  FIRST TRUST ADVISORS L.P. and
                                  THE CHARGER CORPORATION
                                  Date: January 22, 2013


                                  By: /s/ Mark R. Bradley
                                      ---------------------------
                                            Mark R. Bradley
                                      Chief Financial Officer and
                                      Chief Operating Officer of
                                      First Trust Portfolios L.P. and
                                      First Trust Advisors L.P., and
                                      Chief Financial Officer and
                                      Treasurer of The Charger Corporation



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