EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
     PURSUANT TO RULE 13a-14(b) OR RULE 15d-14(b) AND 18 U.S.C. SECTION 1350

In connection with the Quarterly Report on Form 10-Q of The Meridian Resource
Corporation (the "Company") for the quarter ended September 30, 2005, as filed
with the Securities and Exchange Commission on the date hereof (the "Form
10-Q"), I, Joseph A. Reeves, Jr., Chief Executive Officer of the Company,
certify pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1.    The Form 10-Q fully complies with the requirements of Section 13(a) or
      15(d) of the Securities Exchange Act of 1934; and

2.    The information contained in the Form 10-Q fairly presents, in all
      material respects, the financial condition and results of operations of
      the Company.

      Date: November 8, 2005

                                            /s/ Joseph A. Reeves, Jr.
                                            --------------------------------
                                            Joseph A. Reeves, Jr.
                                            Chief Executive Officer