Young motorcycle racer Takuya Yamashiro sees a UFO falling to Earth, a space warship named the Marveller. Takuya's father Dr. Hiroshi Yamashiro, a space archaeologist, investigates the case, but is killed upon finding the spaceship. The incident also attracts the attention of Professor Monster and his evil Iron Cross Army (鉄十字団, Tetsu Jūji Dan), an alien group that plans to rule the universe.

Takuya follows his father to the Marveller and discovers Garia, the last surviving warrior of Planet Spider, a world that was destroyed by Professor Monster and the Iron Cross Army. Garia explains that he was hunting Prof. Monster but now needs someone to carry on the fight and he injects Takuya with some of his own blood. The blood of a person from Planet Spider gives Takuya spider-like powers. Garia then gives Takuya a bracelet that activates his spider protector costume, shoots web-lines, and controls the Marveller ship (which can also transform into a giant battle robot called "Leopardon"). Using his powers, Takuya fights Professor Monster's army and other threats to Earth under the name Spider-Man.