Frontier Oil (FTO) 10-K 2008 FY Annual report

EXHIBIT 32.2

Certification Of Chief Financial Officer Pursuant To

18 U.S.C. Section 1350,

As Adopted Pursuant To

Section 906 Of The Sarbanes-Oxley Act Of 2002

In connection with the Annual Report of Frontier Oil Corporation (the “Company”) on Form 10-K for the period ended December 31, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Doug S. Aron, Executive Vice President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, that:

(1) The Report 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 Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/ Doug S. Aron

Doug S. Aron

Executive Vice President and

Chief Financial Officer

February 26, 2009