Snagglepuss no sooner hears a police report that Mugsy, Public Enemy Number One, is at large when Mugsy and fellow ruffian McGoofy enter Snag's house. Snagglepuss hides in the closets, disguises himself as a lion rug and tries other ruses to avoid detection.

Two escaped convicts are found hiding in a rocket ship built by a renegade inventor, who forces them to become the crew for a trip to the Moon. Also on board, as inadvertent stowaways, are his assistant and his secretary; and none of them are aware that the inventor is actually a Lunarian explorer sent to Earth by the dying Lunar civilization.