Exhibit 4.5


 


ANNEX
A


 


FORM
OF NON-TRANSFERABLE SUBSCRIPTION CERTIFICATE


   


For
use by Zion Oil & Gas acting as Subscription Agent


 


ZION
OIL & GAS, INC.


 


NON-TRANSFERABLE
SUBSCRIPTION CERTIFICATE FOR RIGHTS OFFERING


FOR
HOLDERS OF RECORD ON March 12, 2018


 


ZION
OIL & GAS, INC. (the “Company”) is conducting a rights offering (the “Rights Offering”) that entitles
the holders of the Company’s common stock, $0.01 par value per share (the “Common Stock”), as of the close of
business on March 12, 2018 (the “Record Date”), to receive 0.10 (one tenth) of a subscription right (each,
a “Right”) for each share of Common Stock held of record on the Record Date (i.e., ONE subscription right for
each TEN shares). Each whole Right entitles the holder to subscribe for and purchase one (1) Right (each a “Right”)
of the Company’s securities, with each Right consisting of one (1) share of  the Company’s common stock,
par value $0.01 per share (the “Common Stock”) and one (1) Common Shares Purchase Warrant. Each Right may be purchased
at a per Right subscription price of $5.00.


 


If
you exercise your rights in full, you may also exercise an over-subscription right (the “Over-Subscription Right”)
to purchase additional Rights that remain unsubscribed at the expiration of the Rights Offering, subject to availability and allocation
of Rights among persons exercising this Over-Subscription Right. If there is a change of address and you wish to subscribe, please
note the new address on Form 2.  Your records will be updated with the new information.


 


No
fractional subscription rights or fractional Rights will be issued in this offering. Instead, the number of subscription rights
will be rounded down to the next lowest whole number.


 


For
a more complete description of the terms and conditions of the Rights Offering, please refer to the Company’s Prospectus
Supplement dated April 2, 2018 (the “Prospectus”), which is incorporated herein by reference. Copies of the prospectus
are available upon request from D.F. King, toll free at 866-796-1292 or if you are a bank or broker at 212-269-5550. E-mail address
is zion@dfking.com.


 


This
subscription certificate (the “Rights Certificate”) must be received by American Stock Transfer & Trust Company,
LLC with payment in full by 5:00 p.m., Eastern Standard Time, on May 31, 2018 (unless extended in the sole discretion
of the Company) (the “Expiration Date”). Any Rights not exercised prior to the Expiration Date will be null and void.
Any subscription for Rights in the Rights Offering made hereby is irrevocable.


 


The
Rights represented by this Rights Certificate may be exercised by duly completing Form 1. Rights holders are advised to review
the Prospectus before determining whether to exercise their Rights. In addition, if certificates representing the shares of Common
Stock included in the Right are to be issued are to be sent to an address other than that shown on the Subscription Right Certificate,
also complete Form 2.


 


SUBSCRIPTION
PRICE: $5.00 PER RIGHT


 


The
registered owner whose name is inscribed hereon is entitled to subscribe for Rights upon the terms and subject to the conditions
set forth in the Prospectus and instructions relating to the use hereof.


 


Except
in limited circumstances described in the Prospectus, only you may exercise your Rights.


 


Rights
holders should be aware that if they choose to exercise only part of their Rights, they may not receive a new Rights Certificate
in sufficient time to exercise the remaining Rights evidenced thereby.            


 




     

     


    


 


	American
Stock Transfer & Trust Company, LLC

        Operations
        Center

        Attn:
        Reorganization Department

        6201
        15th Avenue

        Brooklyn,
        New York 11219



 


PLEASE
PRINT ALL INFORMATION CLEARLY AND LEGIBLY.


 


	FORM
                                         1-EXERCISE OF SUBSCRIPTION RIGHTS

                                                                      


To
subscribe for shares/warrants pursuant to your Basic Subscription Right, please complete lines (a) and (c) and sign under Form
3 below. To subscribe for shares/warrants pursuant to your Over-Subscription Right, please also complete line (b) and sign under
Form 3 below.

 


(a)
EXERCISE OF BASIC SUBSCRIPTION RIGHT:

 


I
apply for ______________ rights x $ 5.00= $_______________


                    (shares/warrants)(subscription
price)(amount enclosed)


 

(b)
EXERCISE OF OVER-SUBSCRIPTION RIGHT

 


If
you have exercised your Basic Subscription Right in full and wish to subscribe for additional shares/warrants in any amount
pursuant to your Over-Subscription Right:


 

I
apply for ______________ rights x $ 5.00= $_______________


                  (shares/warrants)(subscription
price)(amount enclosed)


 

(c)
Total Amount of Payment Enclosed = $__________________


 

METHOD
OF PAYMENT (CHECK ONE)


 


☐  Check
or bank draft payable to “American Stock Transfer & Trust Company, LLC as Subscription Agent.”


 

☐   Wire
transfer of immediately available funds directly to the account maintained by American Stock Transfer & Trust Company, LLC,
as Subscription Agent, for purposes of accepting subscriptions in this Rights Offering at JPMorgan Chase Bank, 55 Water Street,
New York, New York 10005, ABA #021000021, Account # 530-354616 American Stock Transfer FBO Zion Oil & Gas, Inc., with reference
to the rights holder's name.




 


 


 


 


 


Telephone
#____________________________


 


Email
Address___________________________

	FORM
                                         2-DELIVERY TO DIFFERENT ADDRESS

                                                                                                                 


If
you wish for the Common Stock/Warrants underlying your subscription rights, a certificate representing unexercised
subscription rights or the proceeds of any sale of subscription rights to be delivered to an address different from that
shown on the face of this Subscription Rights Certificate, please enter the alternate address below, sign under Form 3 and
have your signature guaranteed under Form 4.


___________________________________________


___________________________________________


___________________________________________


 


FORM
3-SIGNATURE

 


TO
SUBSCRIBE: I acknowledge that I have received the Prospectus for this Rights Offering and I hereby irrevocably subscribe for the
number of rights indicated above on the terms and conditions specified in the Prospectus. By signing below I confirm that (1)
after giving effect to the exercise of my Rights, I will not beneficially own, as determined in accordance with Rule 13d-3 under
the Securities Exchange Act of 1934, as amended, more than 14.99% of the Company’s outstanding shares of Common Stock (calculated
immediately upon the closing of the rights offering after giving effect to the Backstop Commitment, as described in the Prospectus)
and (2), if I already beneficially own, as determined in accordance with Rule 13d-3 under the Securities Exchange Act of 1934,
as amended, in excess of 14.99% of the Company’s outstanding shares of Common Stock I will not, via the exercise of the
Rights, increase my proportionate interest in the Company’s Common Stock (with respect to (1) or (2), any such excess shares,
the “Excess Shares”). With respect to any such Excess Shares, I hereby (1) irrevocably appoint and constitute the
Company, each of its authorized officers and their designees, and each of them, with full power of substitution, as my proxy and
attorney in fact with full authority to vote and act by written consent with respect to any such Excess Shares on any matter submitted
to shareholders for a vote or action by written consent, in the discretion of such proxy, to the same extent I would have the
power to vote or act by written consent and (2) grant the Company a right for 90 days from the closing of the rights offering
to repurchase such Excess Rights at the lesser of the $5.00 per right subscription price and the closing price of the Company’s
Common Stock on the NASDAQ on the trading day immediately prior to the date on which notice is sent to the holder of the Company’s
intent to exercise such right, which notice must be sent prior to the expiration of such 90 day period. I agree to cooperate with
the Company and provide to the Company any and all information requested by the Company in connection with the exercise of the
rights granted in the previous sentence.


 


Signature(s):
_______________________________


 

IMPORTANT:
The signature(s) must correspond with the name(s) as printed on the reverse of this Subscription Rights Certificate in every particular,
without alteration or enlargement, or any other change whatsoever.


 

FORM
4-SIGNATURE GUARANTEE

 


This
form must be completed if you have completed Form 2.


 

Signature
Guaranteed: __________________________


                                   (Name
of Bank or Firm)


By:_________________________________________


                                      (Signature
of Officer)


 


IMPORTANT:
The signature(s) should be guaranteed by an eligible guarantor institution (bank, stock broker, savings & loan association
or credit union) with membership in an approved signature guarantee medallion program pursuant to Securities and Exchange Commission
Rule 17Ad-15.





  


FOR
INSTRUCTIONS ON THE USE OF ZION OIL & GAS, INC. SUBSCRIPTION RIGHTS CERTIFICATES, CONSULT D.F. KING, INC., THE INFORMATION
AGENT, AT (866) 796-1292 OR EMAIL: Zion@dfking.com.