AMENDMENT TO STOCK OPTION AGREEMENT AND TERMINATION OF CONTINGENT CONSIDERATION AWARD

Exhibit 10.4

AMENDMENT TO STOCK OPTION AGREEMENT AND TERMINATION OF CONTINGENT CONSIDERATION AWARD

THIS AMENDMENT TO STOCK OPTION AGREEMENT AND TERMINATION OF CONTINGENT CONSIDERATION AWARD (this “Amendment”), dated as of September 16, 2014, is entered into by and between Cerulean Pharma Inc., a Delaware corporation (the “Company”), and Alan Crane (the “Participant”).

WHEREAS, the parties hereto entered into a Nonstatutory Stock Option Agreement (the “Option Agreement”) evidencing the grant by the Company to the Participant on February 7, 2013 of an option to purchase 35,765 shares (the “Shares”) of the Company’s Common Stock, $0.0001 par value per share (“Common Stock”), at an exercise price of $3.92 per Share (in the case of both the number of Shares and exercise price, after giving effect to Company’s reverse stock split that was effected on March 31, 2014), with performance-based vesting;

WHEREAS, the parties hereto entered into a Contingent Consideration Award agreement dated as of February 7, 2013 (the “Award Agreement”), providing, among other things, for cash payments by the Company to the Participant under certain circumstances as described in the Award Agreement; and

WHEREAS, the Company and the Participant desire to (i) amend the Option Agreement (a) to provide for time-based vesting on all Shares and (b) to reduce the number of Shares subject to the Agreement and (ii) to terminate the Award Agreement.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Definitions. Capitalized terms used in this Amendment without definition shall have the respective meanings ascribed thereto in the Option Agreement.

2. Amendments.

(a) Section 1. The first sentence of the first paragraph of Section 1 of the Option Agreement is hereby deleted in its entirety and replaced with the following:

“This agreement evidences the grant by Cerulean Pharma Inc., a Delaware corporation (the “Company” or “Cerulean”), on February 7, 2013 (the “Grant Date”) to Alan Crane, a director of the Company (the “Participant”), of an option to purchase, in whole or in part, on the terms provided herein and in the Company’s 2007 Stock Incentive Plan, as amended (the “Plan”), a total 16,000 shares (the “Shares”) of common stock, $0.0001 par value per share, of the Company (“Common Stock”) at $3.92 per Share.”

(b) Section 2. Section 2 of the Option Agreement is hereby deleted in its entirety and replaced with the following:

“(a) This option will become exercisable (“vest”) as to one-third of the number of Shares on the date of the Company’s annual meeting of stockholders to be held in 2014. This option will vest as to an additional one-third of the original number of Shares on the date of the Company’s annual meeting of stockholders to be held in 2015 and as to the final one-third of the original number of Shares on the date of the Company’s annual meeting of stockholders to be held in 2016. Notwithstanding the foregoing, upon the consummation of a Change of Control Event, the then-remaining unvested portion of the option shall immediately vest and become fully exercisable.

(b) A “Change of Control Event” shall mean (i) the acquisition of beneficial ownership (as defined in Rule 13d-3 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) directly or indirectly by any “person” (as such term is used in Sections 13(d) and 14(d) of the Exchange Act), of securities of the Company representing a majority or more of the combined voting power of the Company’s then outstanding securities, other than an acquisition of securities for investment purposes pursuant to a bona fide financing of the Company; (ii) a merger or consolidation of the Company with any other corporation in which the holders of the voting securities of the Company prior to the merger or consolidation do not own more than 50% of the total voting securities of the surviving corporation; (iii) the sale or disposition by the Company of all or substantially all of the Company’s assets other than a sale or disposition of assets to an entity whose equity interests are held, directly or indirectly, entirely by the same persons and in the same proportions as the equity interests of the Company; or (iv) a change in the composition of the Board of Directors of the Company (the “Board”) that results, during any one year period, in the Continuing Directors no longer constituting a majority of the Board (or, if applicable, the board of directors of a successor corporation to the Company), where the term “Continuing Director” means at any date a member of the Board (x) who was a member of the Board on the Grant Date or (y) who was nominated or elected subsequent to such date by at least a majority of the directors who were Continuing Directors at the time of such nomination or election or whose election to the Board was recommended or endorsed by at least a majority of the directors who were Continuing Directors at the time of such nomination or election; provided, however, that there shall be excluded from this clause (y) any individual whose initial assumption of office after the Grant Date occurred as a result of an actual or threatened election contest with respect to the election or removal of directors or other actual or threatened solicitation of proxies or consents, by or on behalf of a person other than the Board.

(c) The right of exercise shall be cumulative so that to the extent the option is not exercised in any period to the maximum extent permissible it shall continue to be exercisable, in whole or in part, with respect to all Shares for which it is vested until the earlier of the Final Exercise Date or the termination of this option under Section 3 hereof or the Plan.”

3. Termination of Award Agreement. Pursuant to Section 4 of the Award Agreement, the Award Agreement is hereby terminated, effective as of the date hereof.

4. Miscellaneous. Except as specifically provided herein, the Option Agreement remains in full force and effect and is not modified or amended hereby. This Amendment may

be executed (manually or electronically) in counterparts, each of which shall be deemed an original and all of which together shall constitute one and the same instrument. The headings contained in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment. This Amendment shall be governed by, and construed in accordance with, the internal laws of the State of Delaware. From and after the date of this Amendment, all references in the Option Agreement to “this agreement” or “this Agreement” or similar terms shall be deemed to be references to the Option Agreement as amended hereby.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized officers as of the day and year first above written.

[SIGNATURE PAGE TO AMENDMENT TO STOCK OPTION AGREEMENT AND TERMINATION OF CONTINGENT CONSIDERATION AWARD]