On display at the National Museum of Nuclear Science and History in Albuquerque, New Mexico, it’s a Matador cruise missile:
The Matador was the U.S.’ first operational surface-to-surface missile, with an operational concept much like that of the German V-1 missile — but with a twist.
The Matador was tracked by ground radar, and steered by commands from its ground crew. But of course, this left it prone to jamming by its adversaries, and in any event, the radio guidance was only useful for the first 400 km / 250 miles of its (1000 km / 620 mile) range — leaving it to fly on a straight and predictable path for the rest of its flight.
Development of the Matador began in 1945, with its first test flight in 1949. They were deployed in Germany, Taiwan, and South Korea from 1954 through 1962, with 1200 of the craft having been produced. Beginning in 1959, the Matador was replaced by its derivative, the Mace.