CERULEAN PHARMA INC. 840Memorial Drive Cambridge, Massachusetts 02139

EXHIBIT 10.3

CERULEAN PHARMA INC.

840 Memorial Drive

Cambridge, Massachusetts 02139

January 8, 2015

Hercules Technology Growth Capital, Inc.

400 Hamilton Avenue, Suite 310

Palo Alto, California 94301

Attention: Mr. Manuel A. Henriquez

Ladies and Gentlemen:

For good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged by Cerulean Pharma Inc, a Delaware corporation (the “Company”), the Company hereby grants to Hercules Technology Growth Capital, Inc., a Maryland corporation, in its capacity under and pursuant to the Loan Agreement (as defined below) as administrative agent for itself and the Lender (as defined in the Loan Agreement) (“Hercules”), the right to participate in and/or designate one or more of its affiliates (Hercules, together with such affiliates, collectively, “Hercules Purchasers”) to participate in any one or more Subsequent Financings (as defined below) selected by Hercules in its sole discretion by permitting all Hercules Purchasers who participate in such Subsequent Financings to purchase up to a maximum aggregate (for all Subsequent Financings) of $2,000,000.00 of Subsequent Financing Securities (as defined below) therein. Hercules Purchasers shall have no obligation to purchase Subsequent Financing Securities in any Subsequent Financing. Each Hercules Purchaser acquiring Subsequent Financing Securities in a Subsequent Financing shall be an “accredited investor” as defined in Regulation D promulgated under the Securities Act of 1933, as amended (the “Act”).

As used herein:

“Subsequent Financing” means each sale and issuance by the Company on or after the date hereof, in a single transactions or series of related transactions, of shares of its common stock, convertible preferred stock or other equity securities of the Company, whether or not currently authorized (or instruments exercisable for or convertible into shares of common stock, convertible preferred stock or other equity securities of the Company), to one or more accredited investors in a private placement for cash for financing purposes in an offering that is broadly marketed to multiple investors, other than a sale effected pursuant to an effective registration statement under the Act.

“Subsequent Financing Securities” means, with respect to any Subsequent Financing, the class and series of common stock, convertible preferred stock or other equity security of the Company, whether or not currently authorized (or instruments exercisable for or convertible into shares of common stock, convertible preferred stock or other equity securities of the Company), sold and issued by the Company to the investor purchasers in such Subsequent Financing.

The purchase by each Hercules Purchaser of Subsequent Financing Securities in any Subsequent Financing shall be made, subject to the provisions of this letter agreement (and subject to Hercules’ rights set forth in the Loan Agreement (as defined below)), upon the same terms and conditions (including, without limitation, price) as purchases by the other investor purchasers of Subsequent Financing Securities therein, and each such Hercules Purchaser shall execute the definitive stock or securities purchase agreement, investor rights agreement, stockholders agreement, voting agreement and other agreements and documents (collectively, the “Operative Documents”) executed by such other investor purchasers in connection with such Subsequent Financing. As used herein, “Loan Agreement” means that certain Loan and Security Agreement of even date herewith between the Company and Hercules in its capacity as administrative agent for itself and the Lenders as defined therein, as amended and/or restated and in effect from time to time. As used herein, “Warrant” means that certain warrant issued by the Company to Hercules on the date hereof.

The Company shall give Hercules not less than fifteen (15) days’ written notice prior to the anticipated closing of each Subsequent Financing summarizing the principal terms and conditions of such Subsequent Financing (including, without limitation, price), and shall provide such drafts and definitive copies of the Operative Documents and other documents and information in connection with such Subsequent Financing as are provided to the other investor purchasers or prospective investor purchasers of a similar amount of Subsequent Financing Securities therein. Any Hercules Purchaser may exercise its purchase rights hereunder by delivering written notice thereof to the Company no later than the later to occur of (i) five (5) days prior to such anticipated closing, and (ii) ten (10) days after Hercules’ actual receipt of such Company notice. The Operative Documents and other materials and information provided by the Company to Hercules Purchasers in connection with each Subsequent Financing shall be held and treated by each such Hercules Purchaser in confidence in accordance with the provisions of Section 11.12 of the Loan Agreement. All notices and other communications from the Company to Hercules hereunder shall be given in accordance with the requirements of the notice provisions set forth in the Loan Agreement.

This Agreement, and all rights and obligations hereunder, shall terminate upon the earlier of (i) such time when the Hercules Purchasers have purchased $2,000,000.00 of Subsequent Financing Securities in the aggregate, and (ii) the later of (a) the repayment of all indebtedness under the Loan Agreement, and (b) the exercise in full of the Warrant or the expiration or termination of the exercise period for the Warrant.

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This Agreement shall be governed by, and interpreted and enforced in accordance with, the laws of the State of New York, excluding its conflict of laws provisions that would cause the application of the laws of any other jurisdiction.

Acknowledged and agreed to:

[Signature page to Right to Invest Letter]