Rampage World Tour is a updated version of the classic Rampage. Rampage World Tour starts off at Scumlabs International where three lab technicians, George, Lizzy, and Ralph have mutated in an accident involving toxic waste. George has turned into a gigantic ape, Lizzy a gigantic lizard or dinosaur, and Ralph some sort of gigantic wolf. The three destroy the lab they previously worked at and then embark on a path of destruction encompassing the entire globe.

George, Lizzie, and Ralph have been released due to an explosion at a Scumlabs facility. The trio begin to destroy all of Scumlabs' bases scattered throughout the world and kill its employees. In the last levels, Scumlabs CEO Eustace DeMonic turns himself into a monster in an attempt to combat George, Lizzie, and Ralph, but is defeated during a battle on a lunar base. After this, the only surviving Scumlabs employee Dr. Elizabeth Veronica tries to disintegrate the monsters with a ray gun on her spaceship, but it only shrinks them to a miniature size, and they wind up inside her ship. George and Ralph pose on the shelves, while Lizzie bounces atop of Veronica's breasts (though the latter portion is censored on home ports).