The movie begins when Gohan and Oolong search for the Dragon Balls that have all been gathered in the frozen Tsumisumbri Mountains, but before they reach them, Shenron is summoned by Dr. Kochin who wishes that his mentor, Dr. Wheelo, to be released from his icy prison. Gohan and Oolong are then attacked by Kochin's Biomen, but are saved by Piccolo, who easily defeats all of them. As Gohan and Oolong escape however, Piccolo is captured by Dr. Kochin's three Bio-Warriors. Later, Master Roshi is faced by Dr. Kochin's Biomen and defeats them all in battle, but the Biomen kidnap Master Roshi and Bulma, thinking that Roshi is the world's strongest and a suitable body for Dr. Wheelo, whose own body was destroyed, leaving him only as a brain. Roshi is tested by Dr. Kochin's three Bio Warriors, and proves to be worthy, but is ultimately defeated. Bulma inadvertedly reveals that Goku is the strongest, just as the Earth's hero approaches the fortress on the Nimbus Cloud to save his friends.
As soon as Goku arrives, he is attacked by the Bio Warrior Misokattsun, who has a large rubber body. After knocking him down, Goku races inside the fortress and is attacked by large flying balls with spikes. After dodging several of them, Goku fires rapid energy blasts and destroys all of the spikes. Misokattsun then attacks again, but Goku uses the Kaioken attack and flies right through the Bio-Warrior, deflating him. On the higher level, Goku is attacked by Kishime and Ebifurya, and holds his own for a while, but is then shocked by Kishime's electric rods and frozen solid by Ebifurya's icy attack. Gohan and Krillin then arrive to help, but are soon shocked and frozen also. However, Goku uses the Kaioken again, freeing him from his icy prison, and he easily takes out the two Bio-Warriors.
They then arrive at Dr. Wheelo's lab where Bulma is being held, but run into Piccolo, who has been brainwashed. Goku and Piccolo then fight each other, but Gohan's anger causes the mind-controlling device on Piccolo to break. Dr. Kochin tries to shoot Krillin and Bulma with his machine gun-arm, but is beaten by Roshi. Dr. Wheelo then breaks out of the wall, revealing his brain to be inside a huge robot and destroying Kochin in the process, revealing him to be a robot as well. Goku, Gohan, Krillin, Piccolo, and Roshi then fight Dr. Wheelo together, but are unable to win. Goku refuses to give up however, and he decides then to attack Dr. Wheelo with the 3x Kaioken. He manages to break Dr. Wheelo's right arm off and is about to finish him off with the Kamehameha wave when Dr. Wheelo counters it with a blast of his own. Right as Dr. Wheelo is about to win the beam struggle however, Goku uses the 4x Kaioken. He then overpowers Dr. Wheelo's blast and shoots him through his laboratory's ceiling, into space.
All is thought to be over but Dr. Wheelo is still alive and well. Goku senses this and decides the only way to kill Dr. Wheelo is to form a Spirit Bomb. Dr. Wheelo then begins to rain blasts of energy down from space from his claw, which ends up hitting Goku while he is making his Spirit Bomb. This sends Gohan into a rage, and he starts to fly up into the atmosphere to attack Dr. Wheelo, who is already on his way down to earth. Piccolo arrives to assist Gohan, as does Krillin. Gohan and Piccolo stop Dr. Wheelo's descent while Krillin attempts to attack him to no avail. Piccolo attacks Dr. Wheelo with a mouth beam, severely cracking his visor. Back on Earth, Goku is still alive and he launches the Spirit Bomb up into space. Dr. Wheelo out of anger then attempts to destroy the entire planet with the energy built up in his laboratory's power core. He fires off a massive red laser from his entire body down to earth, but Goku's Spirit Bomb collides with the laser, bursting through it, and it hits Dr. Wheelo. He is sent spiraling off into space on a jagged wave of energy where he explodes multiple times until he is no more. In the aftermath of the battle, Piccolo responds to Goku and the others' celebration by saying Gohan deserved all the credit, and the movie ends with everyone laughing (except Piccolo) at how Dr. Wheelo thought that Master Roshi was the strongest man in the world.