This is a test version of the AGM-76A, an air-to-ground version of the Falcon air-to-air missile. The short-lived AGM-76 concept was developed by the Hughes Aircraft Company in 1966.
The AIM-47 air-to-air missile was to be converted into a long range, high-speed, anti-radiation missile called AGM-76 to destroy North Vietnamese surface-to-air missile (SAM) sites. But after the AGM-76 concept was approved by the Air Force, the U.S. Navy promoted an air-to-ground version of their existing Standard missile developed as a surface-launched weapon. A formal competition was established and the Standard won.
Hughes Aircraft donated this AGM-76A to the Smithsonian in 1970.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.