Mitsuo Suwa is an ordinary, somewhat lazy boy whose life changes completely when he meets an alien superhero known as Birdman. Birdman, a member of a galactic peacekeeping federation, selects Mitsuo to become his apprentice on Earth and grants him a special set of equipment. This includes a helmet that multiplies his physical strength by 6600 times, a cape allowing flight at speeds up to 119 kilometers per hour, and a badge that serves as a communicator and also lets him breathe underwater. To protect his new secret identity, he is also given a copy-robot, a doppelgänger that can take his place in everyday life. The penalty for having his identity exposed is severe, originally the destruction of his brain, but later revised to being turned into an animal.

As he begins his duties as Perman, Mitsuo discovers he is not alone. He is joined by other young apprentices who form a small superhero team. The other members are Perman No. 2, a highly intelligent chimpanzee named Booby who communicates through gestures; Perman No. 3, a girl known as Perko who is secretly the famous child actress and idol Sumire Hoshino; and Perman No. 4, a shrewd and business-minded boy named Peryan. In the original manga, a fifth member, a baby named Koichi, is also part of the team. The series follows the daily adventures of this group as they respond to crimes, natural disasters, and various emergencies, all while struggling to maintain their secret lives. A recurring source of comedy and trouble is the copy-robot, which has a mind of its own and often causes confusion for Mitsuo at school or with his friends. A notable narrative arc involves Mitsuo's personal growth as he balances his unrewarding life as a clumsy student with his role as a celebrated hero, at one point even considering abandoning his duties.

One of the most significant storylines concludes with Birdman deciding that one of the Permans must be chosen to travel to his home planet, Bird Star, to train as his successor. Mitsuo is ultimately selected for this honor. After a difficult farewell to his family, friends, and fellow Permans, he leaves Earth. During this emotional departure, Perko reveals her true identity as Sumire Hoshino to him. Mitsuo promises to return as the best Perman he can be, leaving his copy-robot behind to live in his place. While the original manga ends with his departure for advanced training, the television series depicts him remaining on Earth.