As filed with the Securities and Exchange Commission on June 2, 2015.

Registration No. 333-            

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM S-1

REGISTRATION STATEMENT

UNDER

THE SECURITIES ACT OF 1933

NEVRO CORP.

(Exact name of Registrant as specified in its charter)

4040 Campbell Avenue, Menlo Park, CA 94025, (650) 251-0005

(Address, including zip code, and telephone number, including area code, of Registrant’s principal executive offices)

Michael DeMane

Chief Executive Officer

Nevro Corp.

4040 Campbell Avenue, Menlo Park, CA 94025, (650) 251-0005

(Name, address, including zip code, and telephone number, including area code, of agent for service)

Copies to:

Approximate date of commencement of proposed sale to the public: As soon as practicable after this Registration Statement is declared effective.

If any of the securities being registered on this Form are to be offered on a delayed or continuous basis pursuant to Rule 415 under the Securities Act of 1933, check the following box.  ¨

If this Form is filed to register additional securities for an offering pursuant to Rule 462(b) under the Securities Act, please check the following box and list the Securities Act registration statement number of the earlier effective registration statement for the same offering.  x 333-204270

If this Form is a post-effective amendment filed pursuant to Rule 462(c) under the Securities Act, check the following box and list the Securities Act registration statement number of the earlier effective registration statement for the same offering.  ¨

If this Form is a post-effective amendment filed pursuant to Rule 462(d) under the Securities Act, check the following box and list the Securities Act registration statement number of the earlier effective registration statement for the same offering.  ¨

Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, or a smaller reporting company. See the definitions of “large accelerated filer,” “accelerated filer” and “smaller reporting company” in Rule 12b-2 of the Exchange Act.

CALCULATION OF REGISTRATION FEE

The Registration Statement shall become effective upon filing in accordance with Rule 462(b) promulgated under the Securities Act of 1933, as amended.

EXPLANATORY NOTE AND INCORPORATION BY REFERENCE

This registration statement is being filed with respect to the registration of additional shares of common stock, par value $0.001 per share, of Nevro Corp., a Delaware corporation, pursuant to Rule 462(b) promulgated under the Securities Act of 1933, as amended. The contents of the earlier registration statement on Form S-1, as amended (File No. 333-204270), which was declared effective by the Securities and Exchange Commission on June 2, 2015, are incorporated in this registration statement by reference.

The required opinion and consents are listed on an Exhibit Index attached hereto and filed herewith.

SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, as amended, the Registrant has duly caused this Registration Statement on Form S-1 to be signed on its behalf by the undersigned, thereunto duly authorized, in Menlo Park, California, on June 2, 2015.

SIGNATURES

Pursuant to the requirements of the Securities Act of 1933, as amended, this Registration Statement has been signed by the following persons in the capacities and on the dates indicated.

EXHIBIT INDEX