UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 10-K/A

(Amendment No. 1)

For the year ended December 31, 2014

OR

Commission File Number: 001-36715

NEVRO CORP.

(Exact name of registrant as specified in its charter)

4040 Campbell Avenue

Menlo Park, California 94025

(Address of principal executive offices and zip code)

(650) 251-0005

(Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Act:

Securities registered pursuant to Section 12(g) of the Act: None

Indicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule 405 of the Securities Act.    Yes  ¨    No  x

Indicate by check mark if the registrant is not required to file reports pursuant to Section 13 or Section 15(d) of the Exchange Act of 1934 (the “Exchange Act”).     Yes  ¨    No  x

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Exchange Act during the preceding 12 months (or for such shorter period that the registrant was required to file such reports) and (2) has been subject to such filing requirements for the past 90 days.    Yes  x    No  ¨

Indicate by check mark whether the Registrant has submitted electronically and posted on its corporate website, if any, every Interactive Data File required to be submitted and posted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the Registrant was required to submit and post such files).    Yes  ¨    No  ¨

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405 of Regulation S-K is not contained herein, and will not be contained, to the best of registrant’s knowledge, in definitive proxy or information statements incorporated by reference in Part III of this Form 10-K or any amendment to this Form 10-K.  x

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.

Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Act).    Yes  ¨    No  x

The registrant was not a public company as of the last business day of its most recently completed second fiscal quarter, and therefore cannot calculate the aggregate market value of its voting and non-voting common equity held by non-affiliates as of such date.

As of February 28, 2015, there were 24,875,156 shares of the registrant’s Common Stock outstanding.

DOCUMENTS INCORPORATED BY REFERENCE

Portions of the registrant’s Proxy Statement for the registrant’s 2015 Annual Meeting of Stockholders are incorporated by reference into Part III of this Form 10-K to the extent stated herein. The Proxy Statement will be filed within 120 days of the registrant’s fiscal year ended December 31, 2014.

EXPLANATORY NOTE

This Amendment No. 1 to the Form 10-K (this “Amendment”) amends the Annual Report on Form 10-K of Nevro Corp. for the year ended December 31, 2014 filed on March 18, 2015 (the “Form 10-K”) for the sole purpose of refiling Exhibit 10.22 (certain portions of which are omitted pursuant to a confidential treatment request filed with the SEC) and in connection therewith, to amend the Exhibit Index to the 10-K. Pursuant to Rule 12b-15 under the Securities Exchange Act of 1934, as amended, this Amendment also contains new certifications pursuant to Section 302 of the Sarbanes-Oxley Act of 2002, which are attached hereto. Because no financial statements have been included in this Amendment and this Amendment does not contain or amend any disclosure with respect to Items 307 and 308 of Regulation S-K, paragraphs 3, 4, and 5 of the certifications have been omitted.

No other changes have been made to the Form 10-K. This Amendment does not reflect events that may have occurred subsequent to the original filing date, and does not modify or update in any way the disclosures made in the original Form 10-K.

Exhibit Index

SIGNATURES

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 thereunto duly authorized.