This is the launch support structure for the Little Joe II, a test vehicle for launching Apollo "boilerplate" command modules to test the Launch Escape System. NASA launched five Little Joe II vehicles from 1963 to 1966 at the White Sands Missile Range, New Mexico, probably from this structure.
NASA transferred the Little Joe II and its launcher to the Smithsonian in 1974.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.