Appare-Ranman! follows the unlikely duo of Appare Sorrano, an eccentric inventor, and Kosame Ishikki, a cautious samurai. Appare dreams of grand inventions and space travel, while Kosame is tasked with reining in Appare's wild ideas.
An accident leaves them stranded and eventually leads them to Los Angeles. Penniless and far from home, they decide to enter the Trans-America Wild Race.
Appare sees the race as an opportunity to build his own car, and Kosame hopes the prize money will allow them to return to Japan. Their journey becomes a challenging race across America, filled with rivals and dangers lurking in the untamed wilderness.
The story explores whether they will be able to achieve their respective goals and the adventures they will encounter along the way.