Mr. Peabody is a talking dog who is the smartest being in the world. As a puppy, he was rejected by every potential owner, leading him to devote his life to science, athletics and technological discoveries. One day, Peabody finds an orphaned infant and legally adopts him under the name of Sherman. He tutors Sherman through a series of adventures throughout history with the use of the WABAC (pronounced way-back), a time machine and his greatest invention. After narrowly escaping the French Revolution, Sherman starts his first day of school and falls into conflict with classmate Penny Peterson, who he innocently showed up in history class with his first-hand knowledge of George Washington. Penny bullies and humiliates Sherman, insulting him by calling him a "dog" for being raised by one, which provokes Sherman into biting her. Peabody visits Principal Purdy about the matter, but is confronted by Ms. Grunion, a bigoted child and family services agent who threatens to reclaim Sherman if an upcoming home inspection is deemed unfit for him.
Peabody invites the Petersons over for a dinner party to mend fences between the children. While Peabody charms Paul and Patty, Sherman is left with Penny. Sherman reveals the WABAC to Penny after she calls him a liar about his first hand knowledge and they joyride in it, despite Peabody's warnings. Moments later, Sherman seeks Peabody's help to retrieve Penny, who refused to leave her engagement with King Tut in Ancient Egypt. Penny changes her mind when she learns Tut will die young and she will be executed and buried with him. Peabody and Sherman are trapped in a tomb. They escape and impersonate the god Anubis to call off the wedding. Their cover is blown at the last second, but they escape in the WABAC along with Penny.
With the WABAC low on energy, the three stop in Renaissance Florence to seek the aid of Leonardo da Vinci. While Peabody and Leonardo build a contraption to recharge the WABAC, Penny convinces Sherman to explore Leonardo's workshop with her and they bond by using Leonardo's flying machine without permission. They crash-land and Leonardo is thrilled that the machine worked but Peabody is angered at Penny for making Sherman do that. During the return trip to the present, Penny reveals Ms. Grunion's intention of reclaiming Sherman. An argument ensues between Peabody and Sherman while the WABAC draws near a black hole. They escape but crash-land in the Trojan War, where an upset Sherman runs away to join the armies of King Agamemnon. When Peabody and Penny come to retrieve him in the Trojan Horse, they find themselves in the battle and Penny becomes trapped in the Trojan Horse as it races towards a cliff. In a rescue attempt, Sherman and Penny are saved, but Peabody appears to have gone down with the horse and is presumed dead.
Desperate to save Peabody, Sherman and Penny return to the present minutes before Sherman returned the first time to get Peabody to remedy the situation. However, the present copies of Peabody and Sherman show up along with Ms. Grunion. She attempts to reclaim both Shermans, which causes them along with the copies of Peabody to merge and disrupt the space-time continuum. Ms. Grunion makes another attempt at reclaiming Sherman, hurting him in the process which causes an enraged Peabody to revert to his natural instinct and bite her. As Ms. Grunion informs the police, Peabody, Sherman, and Penny flee to the WABAC. They are unable to travel back in time as several historic figures and monuments rain down into the present. The WABAC eventually crashes in the street as the police converge on the WABAC. Peabody is apprehended by Animal Control who plan on euthanizing him for assaulting Ms. Grunion. Sherman protests by explaining that everything that happened is his fault and declares that he would rather be a dog as good as Peabody than a person. Moved by his speech, every historical figure present, the Petersons, and even the police officers concur. George Washington, Abraham Lincoln, and Bill Clinton support Peabody's legal custody of Sherman and award Peabody a presidential pardon.
When a vortex in the space-time continuum rips open, Sherman pilots the WABAC while Peabody handles the computations intending to travel to the future by a few minutes and undo the damage with success. The historical figures and monuments return to their respective times with a smitten King Agamemnon dragging Ms. Grunion with him as she swears revenge on Peabody. Although it appears Peabody and Sherman are lost, they return spontaneously as the Petersons look on and celebrate. Sherman, closer to Peabody than ever, returns to school where he has become good friends with Penny. In the final scene, the time periods are contaminated with modern traits and Ms. Grunion marries King Agamemnon.