<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------

                                   FORM 10-Q

<TABLE>
<S>       <C>                                                          <C>
[X]             QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                 FOR THE QUARTERLY PERIOD ENDED MARCH 31, 2000
                                       OR
[ ]            TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
</TABLE>

             FOR THE TRANSITION PERIOD FROM ________ TO ________ .
                         COMMISSION FILE NUMBER 0-8565

                             MARINE PETROLEUM TRUST
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                            <C>
                    TEXAS                                        75-6008017
         (State or other jurisdiction                         (I.R.S. Employer
      of incorporation or organization)                     Identification No.)
            BANK OF AMERICA, N.A.                                75283-0241
        P.O. BOX 830241, DALLAS, TEXAS                           (Zip Code)
   (Address of principal executive offices)
</TABLE>

       Registrant's telephone number, including area code (800) 985-0794

                                      None
              (Former name, former address and former fiscal year
                         if changed since last report)
                             ---------------------

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                             Yes   X       No _____

     Indicate number of units of beneficial interest outstanding as of the
latest practicable date.

<TABLE>
<CAPTION>
         Title of Each Class of Units              Number of Units of Beneficial Interest
            of Beneficial Interest                             March 31, 2000
         ----------------------------              --------------------------------------
<S>                                            <C>
         UNITS OF BENEFICIAL INTEREST                            2,000,000
</TABLE>

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<PAGE>   2

                             MARINE PETROLEUM TRUST

                                     INDEX

<TABLE>
<CAPTION>
                                                               PAGE
                                                              NUMBER
                                                              ------
<S>                                                           <C>
PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS (UNAUDITED)....................     2

Condensed Consolidated Balance Sheets March 31, 2000 and
  June 30, 1999.............................................     2

Condensed Consolidated Statements of Income and
  Undistributed Income for the Three Months and Nine Months
  Ended March 31, 2000 and 1999.............................     3

Condensed Consolidated Statements of Cash Flows for the Nine
  Months Ended March 31, 2000 and 1999......................     4

Notes to Condensed Consolidated Financial Statements........     5

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
        CONDITION AND RESULTS OF OPERATIONS.................     6

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT
  MARKET RISK...............................................     8

PART II. OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K....................     9

Signatures..................................................    10
</TABLE>
<PAGE>   3

                         PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

                     CONDENSED CONSOLIDATED BALANCE SHEETS
                        MARCH 31, 2000 AND JUNE 30, 1999
                                  (UNAUDITED)

                                     ASSETS

<TABLE>
<CAPTION>
                                                               MARCH 31      JUNE 30
                                                                 2000          1999
                                                              ----------    ----------
<S>                                                           <C>           <C>
Current Assets:
  Cash and cash equivalents.................................  $1,803,426    $1,659,864
  Oil and gas royalties receivable..........................     637,031       307,657
  Receivable from affiliate.................................      67,520        80,939
                                                              ----------    ----------
          Total current assets..............................   2,507,977     2,048,460
                                                              ----------    ----------
Investment in affiliate.....................................     316,041       322,070
Office equipment, net.......................................         555           555
Producing oil and gas properties............................           7             7
                                                              ----------    ----------
                                                              $2,824,580    $2,371,092
                                                              ==========    ==========

                             LIABILITIES AND TRUST EQUITY

Current Liabilities:
  Accounts payable..........................................  $      334    $  244,250
  Income taxes payable......................................       9,096        10,156
                                                              ----------    ----------
          Total current liabilities.........................       9,430       254,406
                                                              ----------    ----------
Trust Equity:
  Corpus -- authorized 2,000,000 units of beneficial
     interest, issued 2,000,000 units at nominal value......           8             8
  Undistributed income......................................   2,815,142     2,116,678
                                                              ----------    ----------
          Total trust equity................................   2,815,150     2,116,686
                                                              ----------    ----------
                                                              $2,824,580    $2,371,092
                                                              ==========    ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        2
<PAGE>   4

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

      CONDENSED CONSOLIDATED STATEMENTS OF INCOME AND UNDISTRIBUTED INCOME
       FOR THE THREE MONTHS AND NINE MONTHS ENDED MARCH 31, 2000 AND 1999
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                       THREE MONTHS               NINE MONTHS
                                                  -----------------------   -----------------------
                                                     2000         1999         2000         1999
                                                  ----------   ----------   ----------   ----------
<S>                                               <C>          <C>          <C>          <C>
Income:
  Oil and gas royalties.........................  $1,502,621   $  648,852   $3,551,456   $2,161,149
  Equity in earnings of affiliate...............      70,727      117,859      241,964      267,766
  Interest income...............................      22,069       23,506       67,388       74,970
                                                  ----------   ----------   ----------   ----------
                                                   1,595,417      790,217    3,860,808    2,503,885
                                                  ----------   ----------   ----------   ----------
Expenses:
  General and administrative....................      55,176       39,260      144,952      141,226
                                                  ----------   ----------   ----------   ----------
  Income before Federal income taxes............   1,540,241      750,957    3,715,856    2,362,659
Federal income taxes of subsidiary..............          --        3,100        2,140        4,200
                                                  ----------   ----------   ----------   ----------
          Net income............................   1,540,241      747,857    3,713,716    2,358,459
Undistributed income at beginning of period.....   2,384,091    1,956,720    2,116,678    1,809,260
                                                  ----------   ----------   ----------   ----------
                                                   3,924,332    2,704,577    5,830,394    4,167,719
Distributions to unitholders....................   1,109,190      610,074    3,015,252    2,073,216
                                                  ----------   ----------   ----------   ----------
Undistributed income at end of period...........  $2,815,142   $2,094,503   $2,815,142   $2,094,503
                                                  ==========   ==========   ==========   ==========
Net income per unit.............................  $     0.77   $     0.37   $     1.86   $     1.18
                                                  ==========   ==========   ==========   ==========
Distributions per unit..........................  $     0.55   $     0.31   $     1.51   $     1.04
                                                  ==========   ==========   ==========   ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        3
<PAGE>   5

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
               FOR THE NINE MONTHS ENDED MARCH 31, 2000 AND 1999
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                 2000           1999
                                                              -----------    -----------
<S>                                                           <C>            <C>
Cash flows from operating activities:
  Net income................................................  $ 3,713,716    $ 2,358,459
  Adjustments to reconcile net income to net cash provided
     by operating activities:
     Equity in undistributed earnings of affiliate..........        6,029        (26,275)
     Change in assets and liabilities:
       Oil and gas royalties receivable.....................     (329,374)       108,908
       Receivables from affiliate...........................       13,419         24,955
       Accounts payable.....................................     (243,916)      (473,832)
       Income taxes payable.................................       (1,060)          (200)
                                                              -----------    -----------
          Net cash provided by operating activities.........    3,158,814      1,992,015
Cash flows from financing activities -- distributions to
  unitholders...............................................   (3,015,252)    (2,073,216)
                                                              -----------    -----------
          Net increase (decrease) in cash and cash
             equivalents....................................      143,562        (81,201)
                                                              -----------    -----------
Cash and cash equivalents at beginning of period............    1,659,864      1,922,336
                                                              -----------    -----------
Cash and cash equivalents at end of period..................  $ 1,803,426    $ 1,841,135
                                                              ===========    ===========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        4
<PAGE>   6

                     MARINE PETROLEUM TRUST AND SUBSIDIARY

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 2000
                                  (UNAUDITED)

ACCOUNTING POLICIES

     The financial statements include the financial statements of Marine
Petroleum Trust (the "Trust") and its wholly-owned subsidiary (Marine Petroleum
Corporation), are condensed, and should be read in conjunction with the Trust's
annual report on Form 10-K for the fiscal year ended June 30, 1999. The
financial statements included herein are unaudited, but in the opinion of
management include all adjustments necessary for a fair presentation of the
results of operations for the periods indicated. Operating results for the three
and nine months ended March 31, 2000 are not necessarily indicative of the
results that may be expected for the year ending June 30, 2000.

UNDISTRIBUTED INCOME

     Undistributed income on March 31, 2000 includes $1,970,931 applicable to
the Trust and $844,211 applicable to Marine Petroleum Corporation. Distributions
to unitholders are dependent on the volume and price of oil and gas sold by
others and will fluctuate from quarter to quarter.

ACCOUNTS PAYABLE

     During the quarter ended March 31, 2000, Marine Petroleum Corporation
determined that $47,000 of the previously established account payable was no
longer required. Accordingly accounts payable was reduced and oil and gas
royalties was increased by $47,000.

                                        5
<PAGE>   7

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

FINANCIAL CONDITION -- LIQUIDITY AND CAPITAL RESOURCES

     The Trust is a "royalty trust" with overriding royalty interests in oil and
gas leases in the Gulf of Mexico. The Trust's indenture (and the charter and
by-laws of its subsidiary) expressly prohibit the operation of any kind of trade
or business. All royalties received by the Trust, less administrative expenses,
are distributed quarterly to unitholders. Since the Trust's sole purpose is to
collect and distribute cash collected from royalties, there are no requirements
for capital.

GENERAL

     Increased oil and gas prices plus an increase in oil production resulted in
a 106% increase in net income for the current quarter as compared to the
comparable quarter a year ago.

     Distributions to unitholders amounted to $.55 per unit this quarter, an
increase of 77% over the distribution for the comparable quarter a year ago.

     The Trust must rely on public records for information regarding drilling
operations. The public records indicate that an estimated 55 drilling and
workover operations have been conducted during the past 9 months on leases in
which the Trust has an interest. These records indicate that over 87% of the
operations resulted in new oil and gas production and over 90% of the operations
were on leases located in the Louisiana offshore area.

     The following table presents the net production quantities of oil and gas
and net income and distributions per unit for the last five quarters.

<TABLE>
<CAPTION>
                                                                PRODUCTION
                                                          ----------------------    NET         CASH
QUARTER                                                   OIL(bbls)    GAS(mcf)    INCOME   DISTRIBUTION
-------                                                   ----------   ---------   ------   ------------
<S>                                                       <C>          <C>         <C>      <C>
March 31, 1999..........................................    17,496      279,145      .37         .31
June 30, 1999...........................................    15,017      147,655      .36         .35
September 30, 1999......................................    23,388      213,537      .54         .44
December 31, 1999.......................................    24,244      180,380      .55         .51
March 31, 2000..........................................    29,549      283,065      .77         .55
</TABLE>

     The Trust's revenues are derived from the oil and gas production activities
of unrelated parties. The Trust's revenues and distributions fluctuate from
period to period based upon factors beyond the Trust's control, including
without limitation the number of productive wells drilled and maintained on
leases subject to the Trust's interest, the level of production over time from
such wells and the prices at which the oil and gas from such wells is sold. The
Trust believes that it will continue to have revenues sufficient to permit
distributions to be made to unitholders for the foreseeable future, although no
assurance can be made regarding the amounts thereof. The foregoing sentence is a
forward-looking statement. Factors that might cause actual results to differ
from expected results include reductions in prices or demand for oil and gas,
which might then lead to decreased production; reductions in production due to
depletion of existing wells or disruptions in service, including as the result
of storm damage to production facilities, blowouts or other production
accidents, and geological changes such as cratering of productive formations;
expiration or release of leases subject to the Trust's interests; and the
discontinuation by parties subject to the contract dated

                                        6
<PAGE>   8

April 30, 1951 between the predecessors of Tidelands Royalty Trust "B"
("Tidelands") and Gulf Oil Corporation of their efforts to obtain leases in the
area that is subject to Tidelands' interests.

     Important aspects of the Trust's operations are conducted by third parties.
As of the date of this report, the Trust has not experienced any significant
disruptions to financial or operating activities as a result of the Year 2000
issues. There were no internal system disruptions and the Trust is not aware of
any failures affecting third parties that conduct the Trust's operations. The
Trust will continue to monitor the situation for any internal or third party
disruptions, but expects none at this time. Costs incurred by the Trust related
to Year 2000 issues were not material.

RESULTS OF OPERATIONS -- THREE MONTHS ENDED MARCH 31, 2000 AND 1999

     Net income for the quarter ended March 31, 2000 amounted to $1,540,241
(including the $47,000 release of the accounts payable reserve) which was
approximately 106% more than the $747,857 (including the $102,000 release of the
accounts payable reserve) realized in the comparable period of 1999.

     Revenue from oil royalties, including the Trust's share of Tidelands'
royalties, increased 427% to $816,879 in the current quarter from $154,944
realized in the comparable period a year ago. As shown in the table below, the
increase in oil royalties over the comparable period a year ago was due to both
increased sales quantities and higher prices.

     Revenue from gas royalties, including the Trust's share of Tidelands'
royalties, increased 25% to $760,299 in the current quarter from $615,354 in the
comparable period a year ago. The gas revenue figures include the additional
revenue from the reduction of the accounts payable reserve as discussed above.
As shown in the table below, there was an increase in gas production and in the
current quarter prices.

     Income from the Trust's equity in Tidelands decreased approximately 40% in
the current period over the comparable period last year due to a decrease in
Tidelands' revenue from natural gas partially offset by an increase in oil
revenue.

     The quantities of oil and gas sold and the average prices realized from
current operations for the three months ended March 31, 2000, and those realized
in the comparable 1999 quarter, are presented in the following table:

<TABLE>
<CAPTION>
                                                                2000        1999
                                                              --------    --------
<S>                                                           <C>         <C>
OIL
  Barrels sold..............................................    29,549      17,496
  Average price.............................................  $  27.64    $   8.86

GAS
  Mcf sold..................................................   283,065     279,979
  Average price.............................................  $   2.52    $   1.83
</TABLE>

RESULTS OF OPERATIONS -- NINE MONTHS ENDED MARCH 31, 2000 AND 1999

     Net income for the nine months ended March 31, 2000 amounted to $3,713,716
(including the $244,250 release of the accounts payable reserve) which was
approximately 57% more than the $2,358,459 (including the $306,000 release of
the accounts payable reserve) realized in the comparable period of 1999.

                                        7
<PAGE>   9

     Revenue from oil royalties, including the Trust's share of Tidelands'
royalties, increased 239% to $1,821,126 in the current nine months from $536,750
realized in the comparable period a year ago. As shown in the table below, the
increase in oil royalties over the comparable period a year ago was due to both
increased sales quantities and higher prices.

     Revenue from gas royalties, including the Trust's share of Tidelands'
royalties, increased 4% to $1,980,282 in the current nine months from $1,911,961
in the comparable period a year ago. The gas revenue figures include the
additional revenue from the reduction of the accounts payable reserve as
discussed above. As shown in the table below, gas production decreased over the
comparable period a year ago, while there was an increase in natural gas prices.

     Income from the Trust's equity in Tidelands decreased approximately 10% in
the current period over the comparable period last year due to a decrease in
Tidelands' revenue from gas partially offset by an increase in oil revenue.

     The quantities of oil and gas sold and the average prices realized from
current operations for the nine months ended March 31, 2000, and those realized
in the comparable 1999 period, are presented in the following table:

<TABLE>
<CAPTION>
                                                                2000       1999
                                                              --------   --------
<S>                                                           <C>        <C>
OIL
  Barrels sold..............................................    77,181     46,721
  Average price.............................................  $  23.60   $  11.49
GAS
  Mcf sold..................................................   676,982    850,394
  Average price.............................................  $   2.56   $   1.89
</TABLE>

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     Not applicable.

                                        8
<PAGE>   10

                           PART II. OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K

     (a) The following exhibits are included herein:

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                             DESCRIPTION OF EXHIBIT
        -------                             ----------------------
<C>                      <S>
          27             -- Financial Data Schedule
</TABLE>

     (b) Current Reports on Form 8-K:

          None

                                        9
<PAGE>   11

                                   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, thereunto duly authorized.

                                            MARINE PETROLEUM TRUST

                                            Bank of America, N.A., Trustee

May 12, 2000                                By:   /s/ CINDY STOVER MILLER
                                              ----------------------------------
                                                     Cindy Stover Miller
                                                        Vice President

May 12, 2000                                         /s/ R. RAY BELL
                                            ------------------------------------
                                                Principal Accounting Officer

                                       10
<PAGE>   12

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                             DESCRIPTION OF EXHIBIT
        -------                             ----------------------
<C>                      <S>
          27             -- Financial Data Schedule
</TABLE>