Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. §1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned principal executive officer of Dearborn Capital Management, L.L.C., the general partner (the “General Partner”) of Grant Park Futures Fund Limited Partnership (“Grant Park”), and principal financial officer of the General Partner hereby certifies that:

(1) the accompanying Annual Report on Form 10-K of Grant Park for the fiscal year ended December 31, 2010 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Grant Park.

Date: February 24, 2011

This certification accompanies this Report pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed filed by Grant Park for purposes of Section 18 of the Securities Exchange Act of 1934, as amended.