Prof. Jaxon Rugarth volunteers for a time-travel experiment at the Time Institute that drives him mad and changes him into the Infinite Man, who can summon any creature from any era to destroy the Legion and Rond Vidar.
A group of Sklarian pirates, a race comprised entirely of females, tangle with the Legion of Super-Heroes. After the Legion handles them, they return to their headquarters to Rond Vidar, who is developing an experiment involving time. With everything set in place, they place the volunteer, Jaxon Rugarth, into Vidar's machine and Rugarth returns as the Infinite Man. The Legion fight Infinite Man and his time-manipulating powers, summoning dinosaurs and other ancient foes. The Legion defeat Infinite Man and Rond Vidar traps him in his machine, hoping to cure him of his predicament.