Prospectus Filed Pursuant to Rule 424(b)(3) (424b3)

Filed Pursuant to Rule 424(b)(3)

Registration No. 333-204905

Prospectus Supplement No. 32

(To Prospectus dated October 14, 2015)

4,000,000 shares of common stock issuable upon the

exercise of the 4,000,000 outstanding Class A warrants

and

2,000,000 shares of common stock issuable upon the

exercise of the 4,000,000 outstanding Class B warrants

This prospectus supplement No. 32 supplements the prospectus dated October 14, 2015 filed pursuant to Rule 424(b)(4) by Cerecor Inc. (the “Company” or “we”), as supplemented by the prospectus supplement No. 1 dated October 20, 2015, the prospectus supplement No. 2 dated November 13, 2015, the prospectus supplement No. 3 dated November 23, 2015, the prospectus supplement No. 4 dated December 17, 2015, the prospectus supplement No. 5 dated December 21, 2015, the prospectus supplement No. 6 dated December 29, 2015, the prospectus supplement No. 7 dated January 5, 2016, the prospectus supplement No. 8 dated January 12, 2016, the prospectus supplement No. 9 dated January 19, 2016, the prospectus supplement No. 10 dated February 2, 2016, the prospectus supplement No. 11 dated April 11, 2016, the prospectus supplement No. 12 dated May 25, 2016, the prospectus supplement No. 13 dated May 26, 2016, the prospectus supplement No. 14 dated May 26, 2016, the prospectus supplement No. 15 dated July 20, 2016, the prospectus supplement No. 16 dated August 15, 2016, the prospectus supplement No. 17 dated August 29, 2016, the prospectus supplement No. 18 dated September 6, 2016, the prospectus supplement No. 19 dated September 12, 2016, the prospectus supplement No. 20 dated September 21, 2016, the prospectus supplement No. 21 dated September 26, 2016, the prospectus supplement No. 22 dated November 8, 2016, the prospectus supplement No. 23 dated November 29, 2016, the prospectus supplement No. 24 dated December 5, 2016, the prospectus supplement No. 25 dated January 20, 2017, the prospectus supplement No. 26 dated January 27, 2017, the prospectus supplement No. 27 dated January 30, 2017, the prospectus supplement No. 28 dated March 2, 2017, the prospectus supplement No. 29 dated March 13, 2017, the prospectus supplement No. 30 dated March 15, 2017 and the prospectus supplement No. 31 dated May 9, 2017 each filed pursuant to Rule 424(b)(3) by the Company (collectively, the “Prospectus”). Pursuant to the Prospectus, this prospectus supplement relates to the continuous offering of 4,000,000 shares of common stock underlying our Class A warrants and 2,000,000 shares of our common stock underlying Class B warrants. Each warrant was a component of a unit that we issued in our initial public offering, which closed on October 20, 2015. The components of the units began to trade separately on November 13, 2015. Each Class A warrant became exercisable on the date when the units detached and the components began to trade separately and will expire on October 20, 2018, or earlier upon redemption. The Class B warrants expired on April 20, 2017.

This prospectus supplement incorporates into our Prospectus the information contained in our attached Current Report on Form 8-K, which was filed with the Securities and Exchange Commission on July 7, 2017.

You should read this prospectus supplement in conjunction with the Prospectus, including any supplements and amendments thereto. This prospectus supplement is qualified by reference to the Prospectus except to the extent that the information in this prospectus supplement supersedes the information contained in the Prospectus.

This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus, including any supplements and amendments thereto.

Our common stock, the Class A warrants and the Class B warrants are traded on The NASDAQ Capital Market under the symbols “CERC,” “CERCW,” and “CERCZ,” respectively.

AN INVESTMENT IN OUR SECURITIES INVOLVES A HIGH DEGREE OF RISK. SEE THE

SECTION ENTITLED “RISK FACTORS” BEGINNING ON PAGE 16 OF THE PROSPECTUS

FOR A DISCUSSION OF INFORMATION THAT SHOULD BE CAREFULLY CONSIDERED IN CONNECTION WITH AN INVESTMENT IN OUR SECURITIES

Neither the Securities and Exchange Commission nor any state securities commission has

approved or disapproved of these securities or determined if this Prospectus is truthful

or complete. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is July 7, 2017

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 8-K/A

(Amendment No. 1)

CURRENT REPORT

Pursuant to Section 13 or 15(d) of

the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): June 30, 2017

Cerecor Inc.

( Exact name of Registrant as Specified in Its Charter)




Delaware	001-37590	45-0705648
(State or Other Jurisdiction of Incorporation)	(Commission File Number)	(IRS Employer Identification No.)



400 E. Pratt Street Suite 606 Baltimore, Maryland		21202
(Address of Principal Executive Offices)		(Zip Code)

Registrant’s Telephone Number, Including Area Code: (410) 522-8707

Not Applicable

(Former Name or Former Address, if Changed Since Last Report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instructions A.2. below):


¨	Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)


¨	Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)


¨	Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))


¨	Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§ 230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§ 240.12b-2 of this chapter).


Emerging growth company	þ

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. £

EXPLANATORY NOTE

This Amendment No. 1 to Current Report on Form 8-K is being filed solely to correct a technical filing error with the original Current Report on Form 8-K filed with the Securities and Exchange Commission on July 7, 2017. No other changes to the original filing are being made by this Amendment No. 1.

Item 5.07. Submission of Matters to a Vote of Security Holders.

On June 30, 2017, Cerecor Inc. (the “ Company ”) held its Annual Meeting. As of May 15, 2017, the record date for the Annual Meeting, there were 14,081,453 shares of common stock outstanding and entitled to vote. At the Annual Meeting, 11,133,848 shares, or approximately 79.1% of the eligible voting shares, were represented either in person or by proxy.

At the Annual Meeting, the Company’s stockholders voted on the following items:


1.	Proposal 1: To elect two nominees to the board of directors to hold office until the 2020 Annual Meeting of Stockholders and until their respective successors are elected and qualified. The following nominees were elected to the Company’s board of directors, with the voting results for each nominee as shown:



	For	Withheld
Isaac Blech	5,233,187	136,386
Phil Gutry	5,233,457	136,116


2.	Proposal 2: To ratify the selection by the Audit Committee of the Board of Directors of the Company of Ernst & Young LLP as the independent registered public accounting firm of the Company for its fiscal year ending December 31, 2017. This proposal was approved by the votes indicated below:



For	Against	Abstain
10,911,369	221,772	707

3.

Proposal 3: To approve, as required by NASDAQ Listing Rules 5635(b) and 5635(d), the issuance to Armistice Capital Master Fund Ltd of up to an aggregate of 26,225,714 shares of common stock, which represents greater than 19.99% of the Company’s outstanding common stock, pursuant to the Securities Purchase Agreement dated April 27, 2017, as more specifically described in our definitive proxy statement filed with the Securities and Exchange Commission on May 23, 2017. This proposal was approved by the votes indicated below:



For	Against	Abstain
2,831,548	164,733	27,578

4.

Proposal 4: To approve a series of alternate amendments to the Company’s Amended and Restated Certificate of Incorporation to effect, at the option of the Board of Directors of the Company, a reverse stock split of the Company’s common stock at a reverse stock split ratio ranging from one-for-two (1:2) to one-for-ten (1:10), inclusive, with the effectiveness of one of such amendments and the abandonment of the other amendments, or the abandonment of all amendments, to be determined by the Board of Directors of the Company prior to the date of the 2018 Annual Meeting of Stockholders, as more specifically described in our definitive proxy statement filed with the Securities and Exchange Commission on May 23, 2017. This proposal was approved by the votes indicated below:



For	Against	Abstain
9,912,694	1,173,665	47,484

5.

Proposal 5: To approve a series of alternate amendments to the Company’s Amended and Restated Certificate of Incorporation to effect, if and only if Proposal 4 is both approved and implemented, a reduction in the total number of authorized shares of the Company’s common stock, as more specifically described in our definitive proxy statement filed with the Securities and Exchange Commission on May 23, 2017. This proposal was approved by the votes indicated below:



For	Against	Abstain
10,626,165	378,663	33,173

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.