The Girl Who Leapt Through Space takes place in the year 311 of the Orbital Calendar, when humanity has established numerous colonies in space. Akiha Shishidou, a resident of one such colony, crosses paths with Leopard, a malevolent artificial intelligence that has infiltrated a colony. Akiha teams up with Itsuki Kannagi, an officer from the Inter-Colony Police, and her companions, which include Honoka Kawai and a robot named Imoko "Imo-chan" Shishidou.