Peabody. who happens to be a dog, is the smartest being in existence. He has accomplished many things in his life as a business magnate, inventor, scientist, Nobel laureate, gourmand, and two-time Olympic medalist. Peabody becomes sad and lonely and decides to adopt his own human son. In an alley, he meets Sherman, a bespectacled, red-haired boy. After saving Sherman from a group of bullies, Peabody discovers that Sherman is an orphan and decides to adopt him.

After a court appearance and a talk with the President and the government, Peabody becomes Sherman's new guardian. Mr. Peabody tells Sherman not to call him "Daddy" and to call him by his name, "Mr. Peabody", or, when speaking informally, "Peabody".

Believing that boys need running room, Peabody invents the WABAC time machine as a birthday gift for Sherman. He and Sherman go back in time to see a Roman speaking in Latin; Peabody adds a translator circuit to the machine so that everyone seems to speak English. They see the Roman again and learn that he is a used chariot salesman. Their next trip is to see Ben Franklin flying his kite that proved lightning was electricity, but Peabody and Sherman discover that they cannot interact with the past. Peabody makes some more adjustments, turning the WABAC into a "should-have-been machine". This causes past events to seem distorted and anachronistic and famous people to behave out of character.