Exhibit 4.1

AMENDMENT TO WARRANT AGENT AGREEMENTS

This Amendment to certain Warrant Agent Agreements (the "Agreements") is made effective as of December 4, 2018, by and between Zion Oil & Gas, Inc., a Delaware corporation having its principal place of business at 12655 North Central Expressway, Suite 1000, Dallas, Texas 75243 (the "Company"), and American Stock Transfer & Trust Company, LLC, a New York limited liability trust company with offices at 6201 15^th Avenue, Brooklyn, NY 11219 (”AST").

WHEREAS, the Company has implemented Agreements with AST as the Company’s Warrant Agent (the “Warrant Agent”), under a Warrant Agent Agreement dated February 2, 2015 for the Warrant ZNWAD, under a Warrant Agent Agreement dated February 1, 2018 for the Warrant ZNWAH, under a Warrant Agent Agreement dated April 2, 2018 for the Warrant ZNWAI and under a Warrant Agent Agreement dated August 21, 2018 for the Warrant ZNWAJ;

WHEREAS, the Warrant ZNWAD has an expiration date of May 2, 2019, the Warrant ZNWAH has an expiration date of April 19, 2019, the Warrant ZNWAI has an expiration date of June 29, 2019 and the Warrant ZNWAJ has an expiration date of October 29, 2019.

WHEREAS, pursuant to Section 3.2 of the Warrant Agent Agreements, the Company in its sole discretion hereby extends the duration of the above Warrants by delaying the Expiration Dates and such extension shall be identical in duration among all of the Warrants and, further, the Company may extend the duration of the Exercise Periods in accordance with Section 3.2 without registered holder consent.

NOW, THEREFORE, in consideration of the mutual agreements herein contained, the parties hereto agree as follows:

 3.2 Duration of Warrants.

Added last paragraph for each Warrant Agent Agreement:

The Company is extending the duration of the Warrant ZNWAD by one (1) year from the expiration date of May 2, 2019 to May 2, 2020.

The Company is extending the duration of the Warrant ZNWAH by one (1) year from the expiration date of April 19, 2019 to April 19, 2020.

The Company is extending the duration of the Warrant ZNWAI by one (1) year from the expiration date of June 29, 2019 to June 29, 2020.

The Company is extending the duration of the Warrant ZNWAJ by one (1) year from the expiration date of October 29, 2019 to October 29, 2020.

IN WITNESS WHEREOF, this Agreement has been duly executed by the parties hereto effective as of the day and year first above written.