EX-4.1


 Exhibit 4.1 

NEITHER THIS WARRANT CERTIFICATE NOR THE WARRANTS REPRESENTED HEREBY NOR ANY SHARES OF COMMON STOCK ISSUABLE UPON THE EXERCISE OF SUCH WARRANTS, NOR ANY
INTEREST IN OR RIGHTS UNDER SAME, HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR THE LAWS OF ANY STATE, AND NEITHER THIS WARRANT CERTIFICATE NOR THE WARRANTS REPRESENTED HEREBY NOR ANY SHARES OF COMMON STOCK ISSUABLE UPON THE EXERCISE OF
SUCH WARRANTS, NOR ANY INTEREST IN OR RIGHTS UNDER SAME, MAY BE SOLD OR OTHERWISE TRANSFERRED UNLESS REGISTERED UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR AN EXEMPTION FROM REGISTRATION IS AVAILABLE. 

W-2016-B-3-     

GALECTIN THERAPEUTICS, INC. 

COMMON STOCK PURCHASE WARRANT – CLASS B-3 

Galectin Therapeutics, Inc., a Nevada corporation (the “Company”), for value received and subject to the terms set forth below
hereby grants to 10X Fund, L.P., a Delaware limited partnership, or its registered successors and assigns (the “Holder”), the right to purchase from the Company at any time or from time to time until the date and time permitted under
Section 2.1 below,                      fully paid and nonassessable shares of the Common Stock, par value $0.001 per share, at the
purchase price of          cents ($            ) per share (the “Exercise Price”). The Exercise Price and the number and
character of such shares of Common Stock purchasable pursuant to the rights granted under this Warrant are subject to adjustment as provided herein. 
 1.
Definitions. As used herein the following terms, unless the context otherwise requires, have the following respective meanings: 

“Common Stock” means the Company’s common stock, par value $0.001 per share, and stock of any other class
of securities into which such securities may hereafter have been reclassified or changed into, including any stock (other than Common Stock) and other securities of the Company or any other Person (corporate or other) which the Holder of this
Warrant at any time shall be entitled to receive, or shall have received, upon the exercise of this Warrant, in lieu of or in addition to Common Stock, or which at any time shall be issuable or shall have been issued in exchange for or in
replacement of Common Stock pursuant to Section 3.2 hereof or otherwise. 
 “Issue Date” means
                    , 2016. 

“Market Value” means, for any date, the price determined by the first of the following clauses that applies:
(a) if the Common Stock is then listed or quoted on a Trading Market (other than the OTC Bulletin Board), the daily volume weighted average price of the Common Stock for such date (or the nearest preceding date) on the Trading Market on which
the Common Stock is then listed or quoted as reported by Bloomberg Financial L.P. (based on a Trading Day from 9:30 a.m. Eastern Time to 4:00 p.m. Eastern Time); (b) if the Common Stock is then listed or quoted on the OTC Bulletin Board, the
average of the high and low price of the Common Stock for such date (or the nearest preceding date) on the OTC Bulletin Board; or (c) if the Common Stock is not then listed or quoted on a Trading Market and if prices for the Common Stock are
then reported in the “Pink Sheets” published by the Pink Sheets, LLC (or a similar organization or agency succeeding to its functions of reporting prices), the most recent bid price per share of the Common Stock so reported. 

  
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 “Registration Rights Agreement” means the Registration Rights
Agreement, dated as of the Issue Date, to which the Corporation and the original Holder are parties, as amended, modified or supplemented from time to time in accordance with its terms. 

“This Warrant” means, collectively, this Warrant and all other stock purchase warrants issued in exchange
therefor or replacement thereof. 
 “Trading Day” means a day on which the common Stock is traded on a
Trading Market. 
 “Trading Market” means any of the following markets or exchanges on which the common
Stock is listed or quoted for trading on the date in question: the Nasdaq SmallCap Market, the NYSE Alternext US, the New York Stock Exchange, the Nasdaq National Market, the OTC Bulletin Board or the “Pink Sheets”. 

2. Exercise. 
 2.1 Exercise Period. The Holder
may exercise this Warrant at any time six months after the Issue Date and before the close of business in Norcross, Georgia on the seventh (7th) anniversary of the Issue Date (the
“Exercise Period”), unless earlier terminated pursuant to Section 2.6 herein. 
 2.2 Exercise Procedure. 

(a) This Warrant will be deemed to have been exercised at such time as the Company has received all of the following items (the “Exercise
Date”): 
 (i) a completed Subscription Agreement as described in Section 2.4 hereof, executed by the Person
exercising all or part of the purchase rights represented by this Warrant (the “Purchaser”); 
 (ii) this Warrant;

 (iii) if this Warrant is not registered in the name of the Purchaser, an Assignment or Assignments in the form set forth
in Exhibit B hereto, evidencing the assignment of this Warrant to the Purchaser together with any documentation required pursuant to Section 8(a) hereof; and 

(iv) a check payable to the order of the Company in an amount equal to the product of the Exercise Price multiplied by the
number of shares of Common Stock being purchased upon such exercise. 
 (b) As soon as practicable after the exercise of this Warrant in full
or in part, and in any event within ten (10) days after the Exercise Date, the Company at its expense will cause to be issued in the name of and delivered to the Purchaser, or as the Purchaser (upon payment by the Purchaser of any applicable
transfer taxes) may direct, a certificate or certificates for the number of fully paid and non-assessable shares of Common Stock to which the Purchaser shall be entitled upon such exercise, together with any other stock or other securities and
property (including cash, where applicable) to which the Purchaser is entitled upon exercise. 
 (c) Unless this Warrant has expired or all
of the purchase rights represented hereby have been exercised, the Company at its expense will, within ten (10) days after the Exercise Date, issue and deliver to or upon the order of the Purchaser a new Warrant or Warrants of like tenor, in
the name of the Purchaser or as the Purchaser (upon payment by the Purchaser of any applicable transfer taxes) may request, calling in the aggregate on the face or faces thereof for the number of shares of Common Stock remaining issuable under this
Warrant. 

  
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 (d) The Common Stock issuable upon the exercise of this Warrant will be deemed to have been
issued to the Purchaser on the Exercise Date, and the Purchaser will be deemed for all purposes to have become the record holder of such Common Stock on the Exercise Date. 

(e) The issuance of certificates for shares of Common Stock upon exercise of this Warrant will be made without charge to the Holder or the
Purchaser for any issuance tax in respect thereof or any other cost incurred by the Company in connection with such exercise and the related issuance of shares of Common Stock. 

(f) The holder represents and warrants that at the time of any exercise of this warrant the holder is an “accredited investor,” as
such term is defined in Rule 501 promulgated under the Securities Act and acknowledges and agrees that the Company may, in its sole discretion, (i) require, as a condition to the exercise of this Warrant, that the holder provide such written
evidence that such holder is an accredited investor as the time of exercise, and (ii) decline to issue the shares of Common Stock issuable upon such exercise if the Company is not satisfied that this warrant may be exercised by the holder
pursuant to a valid registration exemption from the Securities Act and any applicable state securities law. 
 2.3 Acknowledgement of
Continuing Obligations. The Company will, at the time of the exercise of this Warrant, upon the request of the Purchaser, acknowledge in writing its continuing obligation to afford to the Purchaser any rights to which the Purchaser shall continue to
be entitled after such exercise in accordance with the provisions of this Warrant, provided that if the Purchaser shall fail to make any such request, such failure shall not affect the continuing obligation of the Company to afford to the Purchaser
any such rights. 
 2.4 Subscription Agreement. The Subscription Agreement will be substantially in the form set forth in Exhibit A hereto,
except that if the shares of Common Stock issuable upon exercise of this Warrant are not to be issued in the name of the Purchaser, the Subscription Agreement will also state the name of the Person to whom the certificates for the shares of Common
Stock are to be issued, and if the number of shares of Common Stock to be issued does not include all the shares of Common Stock issuable hereunder, it will also state the name of the Person to whom a new Warrant for the unexercised portion of the
rights hereunder is to be delivered. 
 2.5 Fractional Shares. If a fractional share of Common Stock would, but for the provisions of
Section 2.1 hereof, be issuable upon exercise of the rights represented by this Warrant, the Company will, within ten (10) days after the Exercise Date, deliver to the Purchaser a check payable to the Purchaser in lieu of such fractional
share, in an amount equal to the Market Value of such fractional share as of the close of business on the Exercise Date. 
 3. Adjustments. 

3.1 Adjustments for Stock Splits, Etc. If the Company shall at any time after the Issue Date subdivide its outstanding Common Stock, by
split-up or otherwise, or combine its outstanding Common Stock, or issue additional shares of its capital stock in payment of a stock dividend in respect of its Common Stock, the number of shares issuable on the exercise of the unexercised portion
of this Warrant shall forthwith be proportionately increased in the case of a subdivision or stock dividend, or proportionately decreased in the case of a combination, and the Exercise Price then applicable to shares covered by the unexercised
portion of this Warrant shall forthwith be proportionately decreased in the case of a subdivision or stock dividend, or proportionately increased in the case of combination. 

  
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 3.2 Adjustment for Reclassification, Reorganization, Etc. In case of any reclassification,
capital reorganization, or change of the outstanding Common Stock (other than as a result of a subdivision, combination or stock dividend), or in the case of any consolidation of the Company with, or merger of the Company into, another Person (other
than a consolidation or merger in which the Company is the continuing corporation and which does not result in any reclassification or change of the outstanding Common Stock of the Company), or in case of any sale or conveyance to one or more
Persons of the property of the Company as an entirety or substantially as an entirety at any time prior to the expiration of this Warrant, then, as a condition of such reclassification, reorganization, change, consolidation, merger, sale or
conveyance, lawful provision shall be made, and duly executed documents evidencing the same from the Company or its successor shall be delivered to the Holder of this Warrant, so that the Holder of this Warrant shall have the right at any time prior
to the expiration of this Warrant to purchase, at a total price not to exceed that payable upon the exercise of the unexercised portion of this Warrant, the kind and amount of shares of stock and other securities and property receivable upon such
reclassification, reorganization, change, consolidation, merger, sale or conveyance by a holder of the number of shares of Common Stock of the Company as to which this Warrant was exercisable immediately prior to such reclassification,
reorganization, change, consolidation, merger, sale or conveyance, and in any such case appropriate provision shall be made with respect to the rights and interests of the Holder of this Warrant to the end that the provisions hereof (including,
without limitation, provisions for the adjustment of the Exercise Price and of the number of shares purchasable upon exercise of this Warrant) shall thereafter be applicable in relation to any shares of stock, and other securities and property,
thereafter deliverable upon exercise hereof. If, as a consequence of any such transaction, solely cash, and no securities or other property of any kind, is deliverable upon exercise of this Warrant, then, in such event, the Company may terminate
this Warrant by giving the Holder hereof written notice thereof. Such notice shall specify the date (at least thirty (30) days subsequent to the date on which notice is given) on which, at 3:00 P.M., Norcross, Georgia time, this Warrant shall
terminate. Notwithstanding any such notice, this Warrant shall remain exercisable, and otherwise in full force and effect, until such time of termination. 

3.3 Certificate of Adjustment. Whenever the Exercise Price or the number of shares issuable hereunder is adjusted, as herein provided, the
Company shall promptly deliver to the registered Holder of this Warrant a certificate of the Treasurer of the Company, which certificate shall state (i) the Exercise Price and the number of shares of Common Stock issuable hereunder after such
adjustment, (ii) the facts requiring such adjustment, and (iii) the method of calculation for such adjustment and increase or decrease. 

3.4 Small Adjustments. No adjustment in the Exercise Price shall be required unless such adjustment would require an increase or
decrease in the Exercise Price of at least one percent; provided, however, that any adjustments which by reason of this Section 3.5 are not required to be made immediately shall be carried forward and taken into account at the time of exercise
of this Warrant or any subsequent adjustment in the Exercise Price which, singly or in combination with any adjustment carried forward, is required to be made under Sections 3.1 or 3.2.  

4. Reservation of Stock, etc., Issuable on Exercise of Warrant. The Company will at all times reserve and keep available, solely for issuance and
delivery upon the exercise of this Warrant, all shares of Common Stock from time to time issuable upon the exercise of this Warrant. 
 5. Disposition of
This Warrant, Common Stock, Etc. 
 (a) The Holder of this Warrant and any transferee hereof or of the Common Stock with respect to which
this Warrant may be exercisable, by their acceptance hereof, hereby understand and agree that this Warrant and the Common Stock with respect to which this Warrant may be exercisable have not been registered under the Securities Act, and may not be
sold, pledged, hypothecated, donated, or otherwise 

  
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transferred (whether or not for consideration) without an effective registration statement under the Act or an opinion of counsel satisfactory to the Company and/or submission to the Company of
such other evidence as may be satisfactory to counsel to the Company, in each such case, to the effect that any such transfer shall not be in violation of the Act. It shall be a condition to the transfer of this Warrant that any transferee thereof
deliver to the Company its written agreement to accept and be bound by all of the terms and conditions of this Warrant. The foregoing notwithstanding, the Company acknowledges its obligations as set forth in the Registration Rights Agreement to
register the shares of Common Stock issuable upon exercise hereof. 
 (b) Except to the extent the resale of the shares of Common Stock
issuable upon exercise hereof are registered for resale, or may be sold to the public pursuant to Rule 144(b)(1) under the Securities Act, the certificates of the Company that will evidence the shares of Common Stock with respect to which this
Warrant may be exercisable will be imprinted with a conspicuous legend in substantially the following form: 
 “THE SECURITIES
REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), AND MAY NOT BE SOLD, PLEDGED, HYPOTHECATED, DONATED OR OTHERWISE TRANSFERRED (WHETHER OR NOT FOR CONSIDERATION) BY THE
HOLDER WITHOUT AN EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY AND/OR SUBMISSION TO THE COMPANY OF SUCH OTHER EVIDENCE AS MAY BE SATISFACTORY TO COUNSEL TO THE COMPANY, IN EACH SUCH CASE, TO THE
EFFECT THAT ANY SUCH TRANSFER SHALL NOT BE IN VIOLATION OF THE ACT.” 
 Except as set forth in the Registration Rights Agreement, the
Company has not agreed to register any of the Holder’s shares of Common Stock of the Company with respect to which this Warrant may be exercisable for distribution in accordance with the provisions of the Securities Act, and the Company has not
agreed to comply with any exemption from registration under the Act for the resale of the Holder’s shares of Common Stock with respect to which this Warrant may be exercised. Hence, it is the understanding of the Holder of this Warrant that by
virtue of the provisions of certain rules respecting “restricted securities” promulgated by the SEC, the shares of Common Stock of the Company with respect to which this Warrant may be exercisable may be required to be held indefinitely,
unless and until registered under the Securities Act (as contemplated by the Registration Rights Agreement), unless an exemption from such registration is available, in which case the Holder may still be limited as to the number of shares of Common
Stock of the Company with respect to which this Warrant may be exercised that may be sold from time to time. 
 6. Rights and Obligations of Warrant
Holder. The Holder of this Warrant shall not, by virtue hereof, be entitled to any voting rights or other rights as a stockholder of the Company. No provision of this Warrant, in the absence of affirmative actions by the Holder to purchase
Common Stock of the Company by exercising this Warrant, and no enumeration in this Warrant of the rights or privileges of the Holder, will give rise to any liability of such Holder for the Exercise Price of Common Stock acquirable by exercise hereof
or as a stockholder of the Company. 
 7. Transfer of Warrants. Subject to compliance with the restrictions on transfer applicable to this Warrant
referred to in Section 5 hereof, this Warrant and all rights hereunder are transferable, in whole or in part, without charge to the registered Holder, upon surrender of this Warrant with a properly executed Assignment (in substantially the form
attached hereto as Exhibit B), to the Company, and the Company at its expense will issue and deliver to or upon the order of the Holder hereof a new Warrant or Warrants in such denomination or denominations as may be requested, but otherwise of like
tenor, in the name of the Holder or as the Holder (upon payment of any applicable transfer taxes) may direct. 

  
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 8. Replacement of Warrants. Upon receipt of evidence reasonably satisfactory to the Company of the loss,
theft, destruction or mutilation of any Warrant and, in the case of any such loss, theft or destruction, upon delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of any such mutilation, upon
surrender and cancellation of such Warrant, the Company at its expense will execute and deliver, in lieu thereof, a new Warrant of like tenor. 
 9. Company
Records. Until this Warrant is transferred on the books of the Company, the Company may treat the registered Holder hereof as the absolute owner hereof for all purposes, notwithstanding any notice to the contrary. 

10. Miscellaneous. 
 10.1 Notices. All notices and other
communications from the Company to the Holder of this Warrant shall be mailed by first class mail, postage prepaid, to such address as may have been furnished to the Company in writing by such Holder, or, until an address is so furnished, to and at
the address of the last Holder of this Warrant who has so furnished an address to the Company. All communications from the Holder of this Warrant to the Company shall be mailed by first class mail, postage prepaid, to Galectin Therapeutics, Inc.,
4960 Peachtree Industrial Boulevard, Suite 240, Norcross, GA 30071, Attn: 
 Chief Financial Officer, or such other address as may have been furnished to the
Holder in writing by the Company. 
 10.2 Amendment and Waiver. Except as otherwise provided herein, this Warrant and any term hereof may be amended, waived,
discharged or terminated only by an instrument in writing signed by the party against which enforcement of such amendment, waiver, discharge or termination is sought. 

10.3 Governing Law; Descriptive Headings. This Warrant shall be construed and enforced in accordance with and governed by the laws of the State of Delaware.
The headings in this Warrant are for purposes of reference only, and shall not limit or otherwise affect any of the terms hereof. 

[SIGNATURE ON FOLLOWING PAGE] 

  
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 Dated:
                    , 2016. 
  

			
	GALECTIN THERAPEUTICS, INC.
		
	By:	 	 
	Name:	 	
	Title:	 	



  
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 EXHIBIT A 

SUBSCRIPTION AGREEMENT 
 [To be
signed only upon exercise of Warrant] 
  

			
	To:	  	Date:

 The undersigned, the Holder of the within Warrant, pursuant to the provisions set forth in the within Warrant,
hereby irrevocably elects to exercise the purchase rights represented by such Warrant for, and agrees to subscribe for and purchase thereunder,              shares of the Common Stock
covered by such Warrant and herewith makes payment of $             therefor, and requests that the certificates for such shares be issued in the name of, and delivered to,
                    , whose address is:
                    . If said number of shares is less than all the shares covered by such Warrant, a new Warrant shall be registered in the name of
the undersigned and delivered to the address stated below. 
  

			
	Signature	 	 
		
		 	(Signature must conform in all respects to name of Holder as specified on the face of the Warrant or on the form of Assignment attached as Exhibit B thereto.)
		
	Address	 	 
		
		 	 
		
	[Signature Guarantee]	 	



  
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 EXHIBIT B 

ASSIGNMENT 
 [To be signed only
upon transfer of Warrant] 
 For value received, the undersigned hereby sells, assigns and transfers all of the rights of the undersigned
under the within Warrant with respect to the number of shares of the Common Stock covered thereby set forth below, unto: 
  

					
	Name of Assignee	  	Address	  	No. of Shares

  

							
	Dated:	 		 	Signature	 	 
				
		 		 		 	(Signature must conform in all respects to name of Holder as specified on the face of the Warrant.)
				
		 		 	Address	 	 
				
		 		 		 	 
			
		 		 	[Signature Guarantee]


  
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