Parallel Petroleum 10-Q 2006 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION

     (Not filed pursuant to the Securities Exchange Act of 1934)

     Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, Larry C. Oldham, the President and Chief Executive Officer of Parallel Petroleum Corporation (“Parallel”), hereby certifies that the Quarterly Report on Form 10-Q of Parallel for the quarter ended September 30, 2006 fully complies with the periodic reporting requirements of the Securities Exchange Act of 1934, as amended, and the information contained in that Form 10-Q Report fairly presents, in all material respects, the financial condition and results of operations of Parallel.

Dated: November 8, 2006

/s/ Larry C. Oldham  

Larry C. Oldham, 

President and Chief Executive Officer 

     A signed original of this written statement required by Section 906 has been provided to Parallel Petroleum Corporation and will be retained by Parallel Petroleum Corporation and furnished to the Securities and Exchange Commission or its staff upon request.