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                                  UNITED STATES

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549


                                    FORM 8-K


                                 CURRENT REPORT

                         PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934


         DATE OF REPORT (Date of earliest event reported): May 13, 2004




                         PARALLEL PETROLEUM CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)


            Delaware                   0-13305               75-1971716
(State or other jurisdiction      (Commission File          (IRS Employer
of Incorporation or organization)      Number)             Identification No.)

1004 N. Big Spring, Suite 400, Midland, Texas                  79701
  (Address of Principal Executive Offices)                   (Zip Code)



       Registrant's telephone number, including area code: (432) 684-3727




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Item 7.  Financial Statements and Exhibits.


          (c)  Exhibits.

               99.1 Press Release dated May 13, 2004 announcing financial
                    results for the first fiscal quarter ended March 31, 2004.


Item 12. Results of Operations and Financial Condition.

     Parallel Petroleum Corporation wishes to disclose its press release, dated
May 13, 2004, relating to its results of operations and financial condition for
the first fiscal quarter ended March 31, 2004, furnished herewith as Exhibit
99.1.

     The information included in this report is being furnished and shall not be
deemed "filed" for purposes of Section 18 of the Securities Exchange Act of
1934, shall not be subject to the liabilities of that section and shall not be
deemed incorporated by reference in any filing under the Securities Act of 1933
or the Securities Exchange Act of 1934, except as shall be expressly set forth
by specific reference in such a filing.

                                       -2-



                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.


                                            PARALLEL PETROLEUM CORPORATION


                                            By:   /s/ Larry C. Oldham
                                                  Larry C. Oldham, President
                                                  and Chief Executive Officer


Dated: May 13, 2004


                                       -3-


                                  EXHIBIT INDEX


Exhibit No.                      Description


99.1           Press Release dated May 13, 2004 announcing  financial results of
               Parallel Petroleum Corporation for the first fiscal quarter ended
               March 31, 2004.




                                       -4-


                                                                    Exhibit 99.1

                                                                   PRESS RELEASE
Parallel Petroleum Corporation
1004 N. Big Spring, Suite 400            Contact:  Cindy Thomason
Midland, TX 79701   (432) 684-3727                 Manager of Investor Relations
http://www.parallel-petro.com                      cindyt@parallel-petro.com

________________________________________________________________________________
                          PARALLEL PETROLEUM ANNOUNCES
                      FIRST QUARTER 2004 FINANCIAL RESULTS

MIDLAND, Texas, (BUSINESS WIRE), May 13, 2004 - Parallel Petroleum Corporation
(NASDAQ: PLLL) today announced its financial results for the first quarter ended
March 31, 2004. In a separate press release dated May 12, 2004, Parallel
announced its operations update.

First Quarter Results

For the three months ended March 31, 2004, Parallel reported net income of $1.5
million, or $.05 per diluted share. Included in net income was $2.7 million of
operating income, after oil and gas hedge payments of $1.1 million. For the
three months ended March 31, 2003, Parallel recorded net income of $2.3 million,
or $.09 per diluted share, which included $4.2 million of operating income,
after oil and gas hedge payments of $1.1 million.

For the first quarter of 2004, Parallel's sales were 161 MBbls of oil and 732
MMcf of natural gas, or 283 MBOE. The average prices the Company received for
its oil and natural gas on an unhedged/hedged basis, respectively, were
$32.93/$25.93 per barrel and $5.21/$5.24 per Mcf, or $32.21/$28.30 per BOE. For
the same period of 2003, oil sales were 154 MBbls at an average unhedged/hedged
price of $32.60/31.80 per barrel and natural gas sales were 782 MMcf at an
average price of $5.82/4.62 per Mcf, or 284 MBOE at $33.66/29.92 per BOE.

Net cash provided by operating activities for the three-month period ended March
31, 2004, was $4.0 million, compared to $3.6 million for the same period of
2003. During the first quarter of 2004, long term debt was reduced $9.8 million
and the Company invested $8.0 million in its oil and gas activities.

Balance Sheet Review

At March 31, 2004, current assets were $10.6 million, which included $3.6
million of cash. Current liabilities were $9.0 million, including current
derivative obligations of $5.2 million and long-term debt stood at $30.0
million. The Company's net capitalized costs associated with its oil and gas
properties and other equipment were $100.0 million. Parallel's stockholders'
equity as of March 31, 2004 was $60.5 million, which includes $5.8 of other
comprehensive loss that is primarily related to the Company's oil and gas
hedges.

2004 Capital Investment Plan

As Parallel announced in its April 14, 2004 press release, the Company increased
its 2004 capital investment budget to $25.3 million, an approximate 50% increase
over the Company's previously reported $17.0 million capital investment budget.
The amount and timing of expenditures are subject to change based upon market
conditions, results of expenditures, new opportunities and other factors.

Parallel expects to fund the $25.3 million budget primarily from its 2004
operating cash flow, which is presently anticipated to be approximately $17.0
million based only on current production and current realized oil and gas prices
and does not include any additional cash flow that may be derived from the
activities associated with the revised budget. The balance will be funded from
the Company's $52.0 million revolving bank facility, of which the Company
currently has $20.0 million available ($22.0 million at March 31, 2004), and
expected cash derived from non-strategic asset divestitures.

                                     -more-


Parallel Petroleum Announces 1Q 2004 Results
May 13, 2004
Page 2


Management Comments

Larry C. Oldham, Parallel's President, commented, "The Company's production in
the first quarter of 2004 was essentially flat to the first quarter of 2003 and
approximately 7% below the fourth quarter of 2003. We expect to see increases in
our production and oil and gas reserves as we accelerate our development
programs on the Fullerton, Diamond M Shallow and Diamond M Deep oil projects."

Oldham also noted, "On a geographic basis, approximately 71% of our projected
$25.3 million 2004 capital investment budget will be directed toward oil and gas
projects in the Permian Basin of west Texas and New Mexico, 11% to gas projects
in east Texas and the Yegua/Frio gas trend onshore the Gulf Coast area of south
Texas, 8% for north Texas Barnett Shale, 6% for Cotton Valley Reef and 4% for
Utah."

In a final comment, Oldham stated, "The Company also has the financial
flexibility to make an acquisition or enter into an exploitation joint venture
arrangement having significant undeveloped reserve potential. We are actively
working on acquisition and exploitation joint venture targets but do not
presently have any definitive agreements in place."

Conference Call and Webcast Information

The Company's management will host a conference call to discuss its financial
and operational results for the first quarter ended March 31, 2004, on Friday,
May 14, 2004, at 10:00 a.m. Central time. To participate in the call, dial
1-800-884-5695 or 1-617-786-2960, Participant Passcode 74027939, at least five
minutes before the scheduled start time. The conference call will also be
webcast, complete with the "Current Slide Presentation", and can be accessed
live at Parallel's web site, www.parallel-petro.com. A replay of the conference
call will be available at the Company's web site or by calling 1-888-286-8010 or
1-617-801-6888, Passcode 12099787.



                    FINANCIAL STATEMENTS AND SCHEDULES FOLLOW

                         PARALLEL PETROLEUM CORPORATION
                    CONDENSED CONSOLIDATED BALANCE SHEET DATA
                              (dollars in millions)



                                                               March 31,          December 31,
                                                                  2004               2003
                                                              -----------        --------------
                                                              (unaudited)
                                                                             
ASSETS
Current assets                                                $  10.6              $  23.6
Net property and equipment                                      100.0                 94.0
Other assets, net                                                 0.8                  0.7
                                                              -------              -------
 Total                                                        $ 111.4              $ 118.3
                                                              =======              =======
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities                                           $   9.0              $   7.2
Long-term debt, net                                              30.0                 39.8
Deferred tax                                                      6.2                  5.8
Other liabilities                                                 5.7                  4.3
Stockholders' equity                                             60.5                 61.2
                                                              -------              -------
 Total                                                        $ 111.4              $ 118.3
                                                              =======              =======




________________________________________________________________________________

                                     -more-


Parallel Petroleum Announces 1Q 2004 Results
May 13, 2004
Page 3

                         PARALLEL PETROLEUM CORPORATION
                  CONDENSED CONSOLIDATED INCOME STATEMENT DATA
                                   (Unaudited)
                      (in millions, except per share data)


                                                                                         Three Months Ended March 31,
                                                                                      -----------------------------------
                                                                                           2004                 2003
                                                                                      -------------         -------------

                                                                                                      
Oil and gas revenues                                                                        $ 8.0                $ 8.5
Total costs and expenses                                                                      5.3                  4.3
                                                                                        ---------            ---------
      Operating income                                                                        2.7                  4.2
                                                                                        ---------            ---------
Total other expense, net                                                                     (0.4)                (0.7)
                                                                                        ---------            ---------
Income before income taxes                                                                    2.3                  3.5
Income tax expense, deferred                                                                 (0.8)                (1.2)
                                                                                        ---------            ---------
Income before cumulative effect of change in accounting principle                             1.5                  2.3
    Cumulative effect on prior years of a change in accounting principle, net of tax            -                 (0.1)
                                                                                        ---------            ---------
      Net income                                                                              1.5                  2.2
Cumulative preferred stock dividend                                                          (0.1)                (0.1)
                                                                                        ---------            ---------
Net income available to common stockholders                                                 $ 1.4                $ 2.1
                                                                                        =========            =========
Net income per common share:
      Basic - after accounting change                                                      $ 0.05               $ 0.10
      Diluted - after accounting change                                                    $ 0.05               $ 0.09
Weighted average common shares outstanding (millions):
      Basic                                                                                  25.2                 21.1
      Diluted                                                                                28.3                 24.0



________________________________________________________________________________

                              PARALLEL PETROLEUM CORPORATION
                               SALES VOLUMES AND PRICE DATA



                                                                        Three Months Ended
                                                  ---------------------------------------------------------------
                                                       3/31/2004            12/31/2003            3/31/2003
                                                  -------------------- --------------------- --------------------
                                                                                    
Sales Volumes:
  Oil (MBbls)                                                  161                   157                  154
  Natural gas (MMcf)                                           732                   874                  782
  Equivalent barrels of oil (MBOE) (a)                         283                   303                  284
  Equivalent barrels of oil (BOE) per day                    3,106                 3,289                3,154
Average Sales Prices:
  per Bbl (unhedged) (b)                                   $ 32.93               $ 26.87              $ 32.60
  per Bbl (hedged) (c)                                     $ 25.93               $ 22.56              $ 31.80
  per Mcf (unhedged) (b)                                   $  5.21               $  5.02              $  5.82
  per Mcf (hedged) (c)                                     $  5.24               $  5.22              $  4.62
  per BOE (unhedged) (b)                                   $ 32.21               $ 28.43              $ 33.66
  per BOE (hedged) (c)                                     $ 28.30               $ 26.77              $ 29.92


------------------
(a)  A BOE means one barrel of oil equivalent  using the ratio of six Mcf of gas
     to one barrel of oil.
(b)  Unhedged price is the actual price received at the wellhead for our oil and
     natural gas.
(c)  Hedged price is the actual  price  received at the wellhead for our oil and
     natural gas plus or minus the settlements on our derivatives.
________________________________________________________________________________


                                     -more-



Parallel Petroleum Announces 1Q 2004 Results
May 13, 2004
Page 4
                         PARALLEL PETROLEUM CORPORATION
                               HEDGING INFORMATION


COSTLESS COLLARS:                                            Houston Ship Channel
                                                                   Gas Price
                                       MMBTU         --------------------------------------
Period of Time                      Natural Gas            Floor               Cap
-------------------------------- ------------------- ------------------ -------------------
                                                                
2004 remainder (a)                    214,000              $4.40              $5.50





SWAPS:                                 Volume                                 Volume
                                       Hedged             Average             Hedged             Average
Period of Time                        Bbl Oil              Price              MMBTU               Price
-------------------------------- ------------------- ------------------ ------------------- -------------------
                                                                                
2004 remainder (a)                    330,000             $24.45             764,000              $4.692
2005                                  365,000             $23.35             180,000              $4.705
2006                                  265,500             $23.04





INTEREST RATE SWAPS:                                       LIBOR             Expected            Expected
                                      Notional             Fixed              Margin              Fixed
Period of Time                        Amount(c)       Interest Rates(d)      Rates(e)        Interest Rates(f)
-------------------------------- ------------------- ------------------ ------------------- -------------------
                                                                                
2004 remainder (a)                  $30,000,000           2.660%              2.500%              5.160%
2005                                $20,000,000           4.050%              2.250%              6.300%
2006 (b)                            $10,000,000           4.050%              2.250%              6.300%


--------------------------------
(a) second quarter through fourth quarter
(b) through December 20, 2006
(c) Based on the anticipated principal reductions under our credit facility.
(d) Parallel's swap contract with BNP Paribas.
(e) Based on the anticipated borrowing base usage under our credit facility
(f) Total of the libor fixed interest rate plus the expected margin rate under
    our credit facility.
    Our loan agreement required the interest rate to not be below 4.50%.
________________________________________________________________________________



The Company

Parallel Petroleum Corporation is headquartered in Midland, Texas and is an
independent energy company primarily engaged in the acquisition, development,
exploration and production of oil and gas using enhanced oil recovery techniques
and 3-D seismic technology. Additional information on Parallel Petroleum
Corporation is available at http://www.parallel-petro.com.

This release contains forward-looking statements subject to various risks and
uncertainties that could cause the company's future plans, objectives and
performance to differ materially from those in the forward-looking statements.
Forward-looking statements can be identified by the use of forward-looking
terminology such as "may," "will," "expect," "intend," "subject to,"
"anticipate," "estimate," "continue," "present value," "future," "reserves",
"appears," "prospective," or other variations thereof or comparable terminology.
Factors that could cause or contribute to such differences could include, but
are not limited to, those relating to the results of exploratory drilling
activity, the company's growth strategy, changes in oil and natural gas prices,
operating risks, availability of drilling equipment, outstanding indebtedness,
changes in interest rates, dependence on weather conditions, seasonality,
expansion and other activities of competitors, changes in federal or state
environmental laws and the administration of such laws, and the general
condition of the economy and its effect on the securities market. While we
believe our forward-looking statements are based upon reasonable assumptions,
these are factors that are difficult to predict and that are influenced by
economic and other conditions beyond our control. Investors are directed to
consider such risks and other uncertainties discussed in documents filed by the
company with the Securities and Exchange Commission.


                                      ###