Mirai Shōnen Conan is based on Hayao Miyazaki's anime series Future Boy Conan, itself an adaptation of the novel The Incredible Tide by Alexander Key. In 2008, a devastating war between two super-powers led to a nearly complete destruction of the Earth. The continents sunk into the oceans, and only a few islands remained. Conan is a boy who grew up on one of those islands, a descendant of one of the survivors of a spaceship crash. He meets a girl named Lana, who later gets kidnapped by soldiers of Industria, a developed island with centralized administration. Conan travels to Industria and is determined to rescue Lana, uncovering a much greater conspiracy in the process.

The game plays like a fairly traditional platformer taking place in predominantly maze-like environments connected by exit areas. Conan can jump, duck, and fight enemies with his fists. He can also use a limited numbers of ranged weapons such as spears.