Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE

OFFICER OF HOLLY ENERGY PARTNERS, L.P.

PURSUANT TO 18 U.S.C. SECTION 1350

In connection with the accompanying report on Form 10-Q for the quarterly period ended June 30, 2011 and filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Matthew P. Clifton, Chief Executive Officer of Holly Logistic Services, L.L.C., the general partner of HEP Logistics Holdings, L.P., the general partner of Holly Energy Partners, L.P (the “Company”), hereby certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 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 results of operations of the Company.