Exhibit 4.1

ZION OIL & GAS, INC.

as Issuer

AND

AMERICAN STOCK TRANSFER & TRUST COMPANY, LLC

as Trustee

AMENDMENT NO. 1 to SUPPLEMENTAL INDENTURE

Dated as of June 22, 2016

$12,000,000 Maximum

$2,500,000 Minimum

12% Convertible Senior Note due 2028

AMENDMENT No. 1 to the SUPPLEMENTAL INDENTURE, dated as of June 22, 2016, between Zion Oil & Gas, Inc., a Delaware corporation (the “Company”), and American Stock Transfer & Trust Company, LLC, as trustee (the “Trustee”) under the Indenture and the Supplemental Indenture, between the Company and the Trustee (as amended or supplemented from time to time in accordance with the terms thereof, the “Original Indenture” and “Supplemental Indenture”).

RECITALS OF THE COMPANY

WHEREAS, the Board of Directors has duly adopted resolutions authorizing the Company to amend the Supplemental Indenture, dated May 31, 2016;

WHEREAS, the Company desires to change to September 1, 2016 the final offering date (if not extended) of its “12% Convertible Senior Notes due 2028” (the “Notes”), the form and substance of such Notes and the terms, provisions and conditions thereof to be set forth as provided in the Original Indenture, the Supplemental Indenture and this Amendment No. 1 to the Supplemental Indenture;

WHEREAS, the Form of Note, the certificate of authentication to be borne by each Note and the Form of Notice of Conversion, Form of Fundamental Change Purchase Notice and Form of Assignment and Transfer contemplated under the terms of the Notes are to be substantially in the forms hereinafter provided and with dates extended as provided in this Amendment; and

WHEREAS, the Company has requested that the Trustee execute and deliver this Amendment to the Supplemental Indenture, and all requirements necessary to make (i) this Amendment to the Supplemental Indenture a valid instrument in accordance with its terms, and (ii) the Notes, when executed by the Company and authenticated and delivered by the Trustee, the valid obligations of the Company, have been performed, and the execution and delivery of this Amendment No. 1 and the Supplemental Indenture have been duly authorized in all respects.

NOW, THEREFORE, THIS AMENDMENT NO. 1 TO THE SUPPLEMENTAL INDENTURE WITNESSETH, for and in consideration of the premises and the purchases of the Notes by the Holders thereof, it is mutually agreed, for the benefit of the Company and the equal and proportionate benefit of all Holders of the Notes, as follows:

This Amendment No. 1 to the Supplemental Indenture amends the Supplemental Indenture dated May 31, 2016 (“Original Supplement Indenture”). This Amendment No. 1 to the Supplemental Indenture should be read in conjunction with the base Indenture effective March 27, 2014. This Amendment No. 1 is incorporated by reference into the Original Supplemental Indenture. This Amendment No. 1 is not complete without except in connection with, the Supplemental Indenture, including any amendments or supplements thereto.

Change of Closing Date, Maturity Date and Interest Payment Date

The Company desires to change the final offering date (if not extended) of the senior convertible bonds to September 1, 2016. Accordingly, the beginning interest accrual date of the senior convertible bonds is changed from September 1, 2016 to October 2, 2016. The maturity date of the convertible bonds is changed from September 1, 2028 to October 2, 2028. The bonds will bear interest from the new date of October 2, 2016, and payable on October 2^nd of each year, beginning on October 2, 2017. The “regular record date” for interest payments shall continue to be 10 business days prior to the payment date. The convertible bonds continue to be redeemable at any time after the third anniversary of their issuance date. The convertible bonds continue to be convertible at any time prior to the close of business on the business day immediately prior to the 30 day period preceding the maturity date.

Accordingly, all references in the Supplemental Indenture, and all Exhibits thereto, are hereby amended as described above. Except for the substitution of the changed dates above, all other features, conditions and terms of the Supplemental Indenture remain unchanged.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to the Supplemental Indenture, dated May 31, 2016, to be duly executed as of the day and year first above written.

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