Exhibit 99.1

Zion Oil Reduces the Exercise Price of Outstanding Warrants

Dallas, Texas and Caesarea, Israel – June 6, 2012: Zion Oil & Gas, Inc. (NASDAQ GM: ZN, ZNWAL, ZNWAW, ZNWAZ) today announced that it has temporarily reduced the exercise price to $1.75 of all of its outstanding publicly traded warrants quoted under the symbols “ZNWAL”, “ZNWAW” and “ZNWAZ until 5:00 p.m. eastern time on August 15, 2012 (the “Expiration Time”). Any and all warrants properly exercised in accordance with their respective terms prior to the Expiration Time will be accepted by Zion at the reduced exercise price and one share of registered common stock per warrant will be issued to the exercising warrant holder. The original exercise price for the ZNWAL Warrants is $3.50; for the ZNWAZ Warrants, $4.00 and for the ZNWAW Warrants is $7.00.

After the Expiration Time, warrants under the symbol ZNWAL will expire with no further value and the exercise prices included in the original terms of the warrants quoted under the symbols ZNWAW and ZNWAZ will be reinstituted. Except for the reduced exercise price of the warrants prior to the Expiration Time, the terms of the Warrants remain unchanged. Holders of Warrants that desire to exercise their Warrants should contact their brokers and instruct them to exercise the Warrants prior to the Expiration Time.

As of today’s date, approximately 9,820,000 ZNWAL Warrants, 504,000 ZNWAW Warrants and 3,295,000 ZNWAZ Warrants are outstanding. Zion’s common stock is listed on the NASDAQ GLOBAL Market under the symbol ZN. Zion recommends that Warrant holders obtain current market quotations for Zion’s securities before deciding whether or not to exercise their Warrants.

Richard Rinberg, CEO of Zion, stated, “In order to progress our drilling program and establish our new drilling company (tentatively named Zion-Lapidoth Drilling), we evaluated different ways to raise capital. We felt that it was important to allow our warrant holders the opportunity to invest in Zion through a temporary warrant reset program. Consequently, we are pleased to offer our warrant holders the opportunity to exercise their warrants at a reduced exercise price of $1.75 and hope that a substantial number of these warrants will be exercised.

We want to be fair to all of Zion’s warrant holders and believe that a reduction to a uniform warrant exercise price for an identical period achieves that aim. In addition to potentially raising a significant amount of capital for Zion, we believe that a reduction in the number of our outstanding warrants will simplify our capital structure and reduce the overhang of those warrants on the Company’s common stock.”

ZION’S BOARD OF DIRECTORS HAS APPROVED THE WARRANT EXERCISE PRICE REDUCTION. HOWEVER, NEITHER ZION NOR ANY OF ITS DIRECTORS, OFFICERS OR EMPLOYEES MAKES ANY RECOMMENDATION AS TO WHETHER TO EXERCISE WARRANTS. EACH HOLDER OF A WARRANT MUST MAKE ITS OWN DECISION AS TO WHETHER TO EXERCISE A WARRANT.

The information above does not constitute an offer to buy or exchange securities or constitute the solicitation of an offer to sell or exchange any securities in Zion.

Zion Oil & Gas, a Delaware corporation, explores for oil and gas in Israel in areas located onshore between Haifa and Tel Aviv. It currently holds three petroleum exploration licenses: the Joseph License (on approximately 83,272 acres) and the Asher-Menashe License (on approximately 78,824 acres) between Netanya, in the south, and Haifa, in the north, and the Jordan Valley License (on approximately 55,845 acres), just south of the Sea of Galilee. The total license area amounts to approximately 218,000 acres.

FORWARD LOOKING STATEMENTS: Statements in this press release that are not historical fact, including statements regarding Zion’s operations, are forward-looking statements as defined in the “Safe Harbor” provision of the Private Securities Litigation Reform Act of 1995. These forward-looking statements are based on assumptions that are subject to significant known and unknown risks, uncertainties and other unpredictable factors, many of which are described in Zion’s periodic reports filed with the SEC and are beyond Zion’s control. These risks could cause Zion’s actual performance to differ materially from the results predicted by these forward-looking statements. Zion can give no assurance that the expectations reflected in these statements will prove to be correct and assumes no responsibility to update these statements.

Zion’s homepage may be found at: www.zionoil.com

Contact:

Zion Oil & Gas, Inc.

6510 Abrams Rd., Suite 300

Dallas, TX 75231

Mike Williams:

Telephone: 214-221-4610

Email: dallas@zionoil.com

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