Exhibit 99.1

Holly Energy Partners, L.P.

Announces Proposed Offering of Senior Notes

DALLAS, TX, February 28, 2012 — Holly Energy Partners, L.P. (NYSE:HEP) (the “Partnership”) announced today that it and its wholly owned subsidiary, Holly Energy Finance Corp., intend to commence an offering of $300 million in aggregate principal amount of senior notes due 2020.

The Partnership intends to use a portion of the net proceeds of this offering to pay the applicable consideration, accrued and unpaid interest on the tendered notes and related fees and expenses in connection with a cash tender offer to purchase any and all of the Partnership’s outstanding 6.25% senior notes due 2015 and consent solicitation from holders of 6.25% senior notes due 2015 and to use the remainder of the net proceeds to pay all or a portion of the principal of the two promissory notes with an aggregate outstanding principal amount of $72.9 million that were issued to wholly-owned subsidiaries of HollyFrontier Corporation in connection with the acquisition of certain pipeline, tankage, loading rack and crude receiving assets located at HollyFrontier Corporation’s El Dorado and Cheyenne refineries and to repay indebtedness under the Partnership’s revolving credit agreement.

This press release shall not constitute an offer to sell, or the solicitation of an offer to buy, any of the securities described herein, nor shall there be any sale of these securities in any state in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of such state. The securities to be offered have not been registered under the Securities Act of 1933 or any state securities laws and may not be offered or sold in the United States absent registration or an applicable exemption from registration requirements. The securities will be offered only to qualified institutional buyers under Rule 144A and to persons outside the United States under Regulation S. This notice is being issued pursuant to and in accordance with Rule 135c under the Securities Act.

About Holly Energy Partners, L.P.:

Holly Energy Partners, L.P., (“HEP”) headquartered in Dallas, Texas, provides petroleum product and crude oil transportation, terminalling, storage and throughput services to the petroleum industry, including HollyFrontier Corporation subsidiaries. HEP owns and operates petroleum product and crude gathering pipelines, tankage and terminals in Texas, New Mexico, Arizona, Washington, Idaho, Oklahoma, Utah, Wyoming and Kansas. In addition, HEP owns a 25% interest in SLC Pipeline LLC, a 95-mile intrastate pipeline system serving refineries in the Salt Lake City, Utah area.

All statements, other than statements of historical fact, included in this press release are forward-looking statements, including, but not limited to, statements identified by the words “anticipate”, “project”, “expect”, “plan”, “goal”, “forecast”, “intend”, “could”, “believe”, “may” and similar expressions and statements regarding our business strategy, plans and objectives for future operations. These statements reflect our current views with respect to

future events, based on what we believe are reasonable assumptions. Certain factors could cause actual results to differ materially from results anticipated in the forward-looking statements. These factors include, but are not limited to: risks and uncertainties with respect to the actual quantities of petroleum products and crude oil shipped on our pipelines and/or terminalled, stored or throughput in HEP’s terminals and tanks; the economic viability of HollyFrontier Corporation, Alon USA, Inc. and HEP’s other customers; the demand for refined petroleum products in markets HEP serves; HEP’s ability to successfully purchase and integrate additional operations in the future; HEP’s ability to complete previously announced or contemplated acquisitions; the availability and cost of additional debt and equity financing; the possibility of reductions in production or shutdowns at refineries utilizing HEP’s pipeline, terminal and tankage facilities; the effects of current and future government regulations and policies; HEP’s operational efficiency in carrying out routine operations and capital construction projects; the possibility of terrorist attacks and the consequences of any such attacks; our ability to consummate the tender offer and notes offering; the impact of fees, expenses and charges related to the financing transactions described in this press release on HEP’s results of operations; general economic conditions; and other financial, operations and legal risks and uncertainties detailed from time to time in HEP’s Securities and Exchange Commission filings. Other factors described herein, or factors that are unknown or unpredictable, could also have a material adverse effect on future results. Please read “Risk Factors” in Item 1A of our Annual Report on Form 10-K for the year ended December 31, 2011. Except as required by securities laws, we do not intend to update these forward-looking statements and information.

FOR FURTHER INFORMATION, Contact:

Bruce R. Shaw, Senior Vice President and Chief Financial Officer

M. Neale Hickerson, Vice President, Investor Relations

Holly Energy Partners, L.P.

214/871.3555

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