In 1964, the United Nations has launched a rocket flight to the Moon. A multi-national group of astronauts in the UN spacecraft land on the Moon, believing themselves to be the first lunar explorers. They discover a Union Flag on the surface and a note naming Bedford and Cavor, claiming the Moon for Queen Victoria. UN authorities trace the aged Bedford now an old man in a mental hospital. The mental hospital staff prevent him from watching the television reports of the expedition because, according to the matron, it "excites him" with his claims to have been on the Moon dismissed as an insane delusion. The UN representatives question him about the Moon and he tells them his story. The rest of the film, as a flashback, shows what Cavor and Bedford did in the 1890s.
In 1899, Arnold Bedford and his fiance Katherine Callender known as Kate meet an inventor, Joseph Cavor, who has invented Cavorite, a substance that will let anything it is applied to or made of deflect the force of gravity and which he plans to use to travel to the Moon. Cavor has already built a spherical spaceship for this purpose, taking Arnold and (accidentally) Kate with him. Whilst exploring the Moon, Bedford and Cavor fall down a vertical shaft and discover to their amazement an insect-oid population, the Selenites, living beneath the surface. (Cavor coins this name for the creatures after the Greek goddess of the moon, Selene). After escaping from the Selenites back to the surface, they discover that their ship, still containing Kate (who stayed behind because Cavor had brought only two spacesuits), has been dragged into their underground city.
The 1890s expedition claim the Moon for Queen Victoria.
The 1960s astronauts find Cavor's party's flag.
Cavor enters the Selenite alien city on the Moon.
The two, following the drag trail, find and enter the city. The city holds a breathable atmosphere, so (unwisely) they take off and leave their spacesuit helmets. They see the city's power station. In the end they reach their ship underground. The Selenites quickly learn English and interrogate Cavor, who believes they wish to exchange scientific knowledge. The more practical Bedford eventually manages to persuade Cavor that the Selenites are interested in conquering Earth using Cavorite. Cavor helps Bedford and Kate to escape, but stays voluntarily on the Moon.
Bedford, along with Kate (who only leaves the ship once, to help repair the damage caused by the Selenites), flies the ship up a vertical shaft, shattering the window cover at the top, and back to Earth. The aged Bedford concludes his story by mentioning that the ship came down in the sea off Zanzibar, and sank, but he and Kate managed to swim ashore. There is no later radio message from Cavor, and his ultimate fate remains unknown.
Back in the present day, Bedford, the UN party and newspaper reporters watch on television the latest events on the Moon where the American astronauts have broken into the Selenite city, only to find it deserted and decaying. Moments later, the ruined city starts to crumble and collapse, forcing the landing crew to beat a hasty retreat, and seconds later is completely destroyed. Bedford realises that the Selenites must have been killed off by Cavor's common cold viruses to which they had no immunity.