AMENDMENT TO INDEPENDENT CONSULTING AGREEMENT

Exhibit 10.4

AMENDMENT TO INDEPENDENT CONSULTING AGREEMENT

THIS AMENDMENT TO INDEPENDENT CONSULTING AGREEMENT (this “Amendment”), dated as of June 19, 2013 (the “Effective Date”), is entered into by and between Thomas McGauley (hereafter “Consultant”) and Galectin Therapeutics, Inc., a Nevada corporation (the “Company”).

WITNESSETH:

WHEREAS, the parties hereto entered into that certain Independent Consulting Agreement, dated September 19, 2012 (the “Consulting Agreement”), pursuant to which Consultant agreed to provide certain services to the Company on the terms and conditions set forth therein; and

WHEREAS, the parties desire to amend the Consulting Services Agreement to include the Recording Rights as set forth herein.

NOW, THEREFORE, in consideration of these premises, the promises hereinafter contained, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to them in the Consulting Agreement.

2. Section 4 of the Consulting Agreement is amended by deleting Paragraphs (a) and (b) in their entirety and the following is substituted therefore for all purposes whatsoever:

“(a) Term. The Initial Term shall begin on the Effective Date and shall end on the first business day following the filing of the 10Q for the Company for the second quarter, 2013 (such first business day being referred to as the “Termination Date”), or such earlier date as this Agreement may be terminated in accordance with Section 5 below.

(b) Consultant’s Services. Through July 1, 2013, Consultant shall provide financial services and serve as the Acting Chief Financial Officer to the Company in furtherance of the Company Business at the discretion of the CEO and in accordance with the business direction provided to Consultant by the CEO. After July 1, 2013 and through the remaining term of this Agreement, Consultant shall no longer be the Acting Chief Financial Officer of the Company, but shall provide the services specified herein as an independent consultant without title. Consultant agrees to devote the time and effort necessary to perform the services requested but in any event, Consultant agrees to be available for at least ninety five (95) hours per month during the Term. Consultant shall carry out all such services in accordance with all applicable laws and regulations governing the business of the Company, any Company Affiliate and Consultant. Consultant shall have discretion in the time, place and manner in which it provides services, giving due regard to the Company’s needs in growing the Company Business.”

3. Section 6 of the Consulting Agreement is deleted in its entirety and the following is substituted therefore for all purposes whatsoever:

6. Rights and Remedies Upon Termination.

“(a) Upon the termination of this Agreement for any reason, including, without limitation, upon the expiration of the then current Term hereof, the parties shall not have any further rights, duties or obligations under this Agreement other than those provided in Sections 9 and 10 below. Notwithstanding the foregoing, the termination of this Agreement may trigger certain rights and obligations of the parties under other agreements, which rights and obligations shall not in any way be altered by this Agreement and may trigger the benefit for Consultant set forth in (b) below. Furthermore, the termination of this Agreement shall not in any way negate the parties’ respective rights, duties or obligations that accrued prior to the termination of this Agreement.

(b) Consultant is hereby granted options to purchase 25,000 shares (the “Options”) of the Company’s common stock under the terms and conditions of the Stock Option Agreement attached hereto as Exhibit A (“Stock Option Agreement”) and Pro-Pharmaceuticals, Inc. Amended and Restated 2009 Incentive Compensation Plan (“Stock Option Plan”). The Stock Option Agreement shall provide for the Options to be 100% vested upon the Termination Date, provided that the Consultant (i) has not been terminated by the Company for Cause or (ii) has not voluntarily terminated this Agreement, in either case prior to the Termination Date, and for Consultant to have the right to a cashless exercise of the Options, in whole or in part.”

4. Section 7 of the Consulting Agreement is hereby amended for all purposes whatsoever by changing the title of said Section to read “Indemnification by Consultant; Indemnification by Company” and the addition of a new subsection (c) as follows:

“(c) The Company shall indemnify and hold harmless the Consultant with respect to any litigation pending as of the termination date of this Agreement and as to which the Consultant is named as a party to such litigation; provided, however, that the obligation of the Company with respect to such indemnification obligation in favor of the Consultant shall, in all events, be limited to the same extent, including without limitation, dollar amount, as the Company would be obligated to indemnify an officer of the Company for the same or comparable claim.”

5. Except as specifically amended by this Amendment, the Consulting Agreement shall continue in full force and effect.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the date first hereinabove set forth by their representatives thereunto duly authorized, to be effective as of the Effective Date.

EXHIBIT A

Stock Option Agreement

[See attached.]

STOCK OPTION AGREEMENT

GALECTIN THERAPEUTICS INC.

STOCK OPTION AGREEMENT

FOR

THOMAS MCGAULEY

AGREEMENT

1. Grant of Option. Galectin Therapeutics Inc., a Nevada corporation (the “Company”) hereby grants, as of the date hereof (“Date of Grant”), to Thomas McGauley (the “Optionee”) an option (the “Option”) to purchase up to twenty-five thousand (25,000) shares of the Company’s common stock, $0.01 par value per share (the “Shares”), at an exercise price per share equal to $         (the “Exercise Price”). The Option shall be subject to the terms and conditions set forth herein. The Option is being issued pursuant to the Company’s 2009 Incentive Compensation Plan (the “Plan”), which is incorporated herein for all purposes. The Option is a Non-Qualified Stock Option and not an Incentive Stock Option. The Optionee hereby acknowledges receipt of a copy of the Plan and agrees to be bound by all of the terms and conditions hereof and thereof and all applicable laws and regulations.

2. Definitions. Unless otherwise provided herein, terms used herein that are defined in the Plan and not defined herein shall have the meanings attributed thereto in the Plan.

3. Exercise Schedule. Except as otherwise provided in Sections 6 or 9 of this Agreement, or in the Plan, the Optionee shall be entitled to exercise the Option at any time after the first business day following the filing of the 10Q for the Company for the second quarter, 2013 (“Vesting Date”). The Option may be exercised by the Optionee, in whole or in part, at any time or from time to time after the Vesting Date and prior to the expiration of the Option as provided herein.

For the avoidance of doubt, in the event that Optionee’s services to the Company pursuant to that certain Independent Consulting Agreement, dated September 19, 2012, between the Company and Optionee (“Consulting Agreement”) is terminated prior to the Vesting Date, other than as a result of (a) termination of Optionee’s services by the Company for Cause (as defined in the Consulting Agreement) or (b) Optionee’s voluntarily termination of his services to the Company provided pursuant to the Consulting Agreement, this Option shall be fully vested.

4. Method of Exercise. The vested portion of this Option shall be exercisable in whole or in part at any time after the Vesting Date by written notice which shall state the election to exercise the Option, the number of Shares in respect of which the Option is being exercised, and such other representations and agreements as to the holder’s investment intent with respect to such Shares as may be required by the Company pursuant to the provisions of the Plan. Such written notice shall be signed by the Optionee and shall be delivered in person or by certified mail to the Secretary of the Company. The written notice shall be accompanied by payment of the Exercise Price as determined pursuant to Section 5 hereof. This Option shall be deemed to be exercised after both (a) receipt by the Company of such written notice accompanied by the Exercise Price and (b) arrangements that are satisfactory to the Committee in its sole discretion have been made for Optionee’s payment to the Company of the amount, if any, that is necessary to be withheld in accordance with applicable

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Federal or state withholding requirements. No Shares shall be issued pursuant to the Option unless and until such issuance and such exercise shall comply with all relevant provisions of applicable law, including the requirements of any stock exchange upon which the Shares then may be traded.

5. Method of Payment. Payment of the Exercise Price shall be by any of the following, or a combination thereof, at the election of the Optionee: (a) cash; or (b) check; or (c) with Shares owned by the Optionee, or the withholding of Shares that otherwise would be delivered to the Optionee as a result of the exercise of the Option or (d) pursuant to a “cashless exercise” procedure, by delivery of a properly executed exercise notice together with such other documentation, and subject to such guidelines, as the Committee shall require to effect an exercise of the Option and delivery to the Company by a licensed broker acceptable to the Company of proceeds from the sale of Shares, or (e) such other consideration or in such other manner as may be determined by the Committee in its absolute discretion.

6. Termination of Option.

(a) General. Any unexercised portion of the Option shall automatically and without notice terminate and become null and void at the tenth (10^th) anniversary of the date as of which the Option is granted.

(b) Cancellation. To the extent not previously exercised, (i) the Option shall terminate immediately in the event of (A) the liquidation or dissolution of the Company, or (B) any reorganization, merger, consolidation or other form of corporate transaction in which the Company does not survive or the Shares are exchanged for or converted into securities issued by another entity, or an affiliate of such successor or acquiring entity, unless the successor or acquiring entity, or an affiliate thereof, assumes the Option or substitutes an equivalent option or right pursuant to Section 10(c)(ii) of the Plan, and (ii) the Committee in its sole discretion may by written notice (“cancellation notice”) cancel, effective upon the consummation of any transaction that constitutes a Change in Control, the Option (or portion thereof) that remains unexercised on such date. The Committee shall give written notice of any proposed transaction referred to in this Section 6(b) a reasonable period of time prior to the closing date for such transaction (which notice may be given either before or after approval of such transaction), in order that the Optionee may have a reasonable period of time prior to the closing date of such transaction within which to exercise the Option if and to the extent that it then is exercisable (including any portion of the Option that may become exercisable upon the closing date of such transaction). The Optionee may condition his exercise of the Option upon the consummation of a transaction referred to in this Section 6(b).

7. Transferability. Unless otherwise determined by the Committee, the Option granted hereby is not transferable otherwise than by will or under the applicable laws of descent and distribution, and during the lifetime of the Optionee the Option shall be exercisable only by the Optionee, or the Optionee’s guardian or legal representative. In addition, the Option shall not be assigned, negotiated, pledged or hypothecated in any way (whether by operation of law or otherwise), and the Option shall not be subject to execution, attachment or similar process. Upon any attempt to transfer, assign, negotiate, pledge or hypothecate the Option, or in the event of any levy upon the Option by reason of any execution, attachment or similar process contrary to the provisions hereof, the Option shall immediately become null and void. The terms of this Option shall be binding upon the executors, administrators, heirs, successors and assigns of the Optionee.

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8. No Rights of Stockholders. Neither the Optionee nor any personal representative (or beneficiary) shall be, or shall have any of the rights and privileges of, a stockholder of the Company with respect to any Shares purchasable or issuable upon the exercise of the Option, in whole or in part, prior to the date on which the Shares are issued.

9. Acceleration of Exercisability of Option.

(a) Acceleration Upon Certain Terminations or Cancellations of Option. So long as this Option has not terminated pursuant to Section 6(a) hereof, this Option shall become immediately fully exercisable immediately prior to the occurrence of any event that would result in (i) the Option being terminated pursuant to Section 6(b)(i) hereof, or (ii) the Company exercising its discretion to provide a cancellation notice with respect to the Option pursuant to Section 6(b)(ii) hereof.

(b) Acceleration Upon Change in Control. Subject to Section 9(a) above and so long as this Option has not terminated pursuant to Section 6(a) hereof, this Option shall become immediately fully exercisable immediately prior to the occurrence of any event that qualifies as a “Change in Control”, as defined in Section 9(b) of the Plan.

10. No Right to Continued Employment. Neither the Option nor this Agreement shall confer upon the Optionee any right to continued employment or service with the Company.

11. Law Governing. This Agreement shall be governed in accordance with and governed by the internal laws of the State of Georgia.

12. Non-Qualified Stock Option Treatment. The terms of this Option shall be interpreted in a manner consistent with the intent of the Company and the Optionee that the Option constitute a Non-Qualified Stock Option.

13. Interpretation / Provisions of Plan Control. This Agreement is subject to all the terms, conditions and provisions of the Plan, including, without limitation, the amendment provisions thereof, and to such rules, regulations and interpretations relating to the Plan adopted by the Committee as may be in effect from time to time. If and to the extent that this Agreement conflicts or is inconsistent with the terms, conditions and provisions of the Plan, the Plan shall control, and this Agreement shall be deemed to be modified accordingly. The Optionee accepts the Option subject to all of the terms and provisions of the Plan and this Agreement. The undersigned Optionee hereby accepts as binding, conclusive and final all decisions or interpretations of the Committee upon any questions arising under the Plan and this Agreement, unless shown to have been made in an arbitrary and capricious manner.

14. Notices. Any notice under this Agreement shall be in writing and shall be deemed to have been duly given when delivered personally or when deposited in the United States mail, registered, postage prepaid, and addressed, in the case of the Company, to the Company’s Secretary at 4960 Peachtree Industrial Blvd., Suite 240, Norcross, GA 30071, or if the Company should move its principal office, to such principal office, and, in the case of the Optionee, to the Optionee’s last

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permanent address as shown on the Company’s records, subject to the right of either party to designate some other address at any time hereafter in a notice satisfying the requirements of this Section.

15. Section 409A.

(a) It is intended that the Option awarded pursuant to this Agreement be exempt from Section 409A of the Code (“Section 409A”) because it is believed that (i) the Exercise Price may never be less than the Fair Market Value of a Share on the Date of Grant and the number of shares subject to the Option is fixed on the original Date of Grant, (ii) the transfer or exercise of the Option is subject to taxation under Section 83 of the Code and Treas. Reg. 1.83-7, and (iii) the Option does not include any feature for the deferral of compensation other than the deferral of recognition of income until the exercise of the Option. The provisions of this Agreement shall be interpreted in a manner consistent with this intention, and the provisions of this Agreement may not be amended, adjusted, assumed or substituted for, converted or otherwise modified without the Optionee’s prior written consent if and to the extent that the Company believes or reasonably should believe that such amendment, adjustment, assumption or substitution, conversion or modification would cause the award to violate the requirements of Section 409A. In the event that either the Company or the Optionee believes, at any time, that any benefit or right under this Agreement is subject to Section 409A, then the Committee may (acting alone and without any required consent of the Optionee) amend this Agreement in such manner as the Committee deems necessary or appropriate to be exempt from or otherwise comply with the requirements of Section 409A (including without limitation, amending the Agreement to increase the Exercise Price to such amount as may be required in order for the Option to be exempt from Section 409A).

(b) Notwithstanding the foregoing, the Company does not make any representation to the Optionee that the Option awarded pursuant to this Agreement is exempt from, or satisfy, the requirements of Section 409A, and the Company shall have no liability or other obligation to indemnify or hold harmless the Optionee or any Beneficiary for any tax, additional tax, interest or penalties that the Optionee or any Beneficiary may incur in the event that any provision of this Agreement, or any amendment or modification thereof or any other action taken with respect thereto, that either is consented to by the Optionee or that the Company reasonably believes should not result in a violation of Section 409A, is deemed to violate any of the requirements of Section 409A.

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IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the – day of             , 2013.

The Optionee acknowledges receipt of a copy of the Plan and represents that he has reviewed the provisions of the Plan and this Option Agreement in their entirety, is familiar with and understands their terms and provisions, and hereby accepts this Option subject to all of the terms and provisions of the Plan and the Option Agreement. The Optionee further represents that he has had an opportunity to obtain the advice of counsel prior to executing this Option Agreement.

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