| (Mark One) |
|------------|
| þ     | ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d)OF THE SECURITIES EXCHANGE ACT OF 1934 |
|       |   |
|       | For the fiscal year ended April 27, 2012 |
|       |                                                                                                                                           or |
| o          | TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)OF THE SECURITIES EXCHANGE ACT OF 1934 |
|       |   |
|       | For the transition period from                                                                to |

| Delaware                                                      | 76-0236465                          |
|---------------------------------------------------------------|-------------------------------------|
| (State or other jurisdiction ofincorporation or organization) | (I.R.S. EmployerIdentification No.) |

| Title of Each Class of Stock                             |   | Name of Each Exchange on Which Registered |
|----------------------------------------------------------|--------|-------------------------------------------|
| Common Stock — $0.01 par value per share |   | The NASDAQ Stock Market LLC               |

| Large accelerated filer | o                                               | Accelerated filer         | þ |
|-------------------------|-------------------------------------------------|---------------------------|--------|
| Non-accelerated filer   | o (Do not check if a smaller reporting company) | Smaller reporting company | o      |

----

----

|   | CYBERONICS, INC. |
|--------|------------------|
|   |             |   |
|   |  By:        | /s/ GREGORY H. BROWNE |
|   |             | Gregory H. Browne |
|   |             | Senior Vice President, Finance and Chief Financial Officer |
|   |             | (Principal Financial Officer and Principal Accounting Officer) |

| Signature                                                           | Title                                                                                                                     | Date          |
|---------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------|---------------|
|                                                                |                                                                                                                      |          |
| /s/  HUGH M. MORRISON*Hugh M. Morrison                    | Chairman of the Board of Directors                                                                                        | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  DANIEL J. MOOREDaniel J. Moore                       | Director, President and Chief Executive Officer(Principal Executive Officer)                                              | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  GREGORY H. BROWNEGregory H. Browne                   | Senior Vice President, Finance and Chief Financial Officer (Principal Financial Officer and Principal Accounting Officer) | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  GUY C. JACKSON*Guy C. Jackson                        | Director                                                                                                                  | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  JOSEPH E. LAPTEWICZ*Joseph E. Laptewicz              | Director                                                                                                                  | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  ALFRED J. NOVAK*Alfred J. Novak                      | Director                                                                                                                  | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  ARTHUR L. ROSENTHAL PH.D.*Arthur L. Rosenthal, Ph.D. | Director                                                                                                                  | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| /s/  JON T. TREMMEL*Jon T. Tremmel                        | Director                                                                                                                  | June 18, 2012 |
|                                                                |                                                                                                                      |          |
| *By: /s/ DANIEL J. MOOREDaniel J. Moore, Attorney-in-fact           |                                                                                                                      |          |
|                                                                |                                                                                                                      |          |
| *By: /s/ GREGORY H. BROWNEGregory H. Browne, Attorney-in-fact       |                                                                                                                      |          |

----