Mr. Peabody is a gifted anthropomorphic dog who has an adopted 7-year-old son, Sherman. He tutors Sherman travelling throughout history using the WABAC, a time machine.
They visit Marie Antoinette in Versailles during the French Revolution in 1789. Getting caught in the Reign of Terror, Peabody is nearly executed by Maximilien Robespierre with a guillotine, but escapes with Sherman through the Paris sewers.
In the present day, Sherman attends the Susan B. Anthony School in New York City. His knowledge of the apocryphal nature of the George Washington cherry-tree anecdote leads to a fight with Penny Peterson in the cafeteria where she puts him in a choke hold. Peabody is called in by Principal Purdy who tells Peabody that Sherman had bit Penny. He is also confronted during this meeting by Ms. Grunion, a Child Protective Services agent, who implies that Sherman’s behavior is due to being raised by a dog. She informs Peabody that she’ll come to their home to investigate whether he is an unfit parent.
Peabody invites Penny and her parents over for a dinner party to reconcile before Ms. Grunion arrives. Penny calls Sherman a liar for claiming first-hand knowledge of history. Despite Peabody’s contrary instructions, Sherman shows Penny the WABAC. Penny goads Sherman into taking her into the past, where she stays in Ancient Egypt in 1,330 BCE to marry King Tut. Sherman returns to get Mr. Peabody’s help. Peabody hypnotises the Petersons, and retrieves Penny by telling her the fate of a pharaoh’s widow.
The WABAC runs out of power, but Peabody is able to get them to Renaissance Florence in 1508 where they meet Leonardo da Vinci. Penny and Sherman explore da Vinci’s attic, finding his flying machine. Penny goads Sherman into flying it, which he manages to do before crashing. Da Vinci is thrilled the device works, but Peabody’s upset that Sherman risked his safety and destroyed an historical artifact.
They again attempt to return, but a black hole forces them into an emergency landing during the Trojan War in 1,184 BCE. Upset about learning what Ms. Grunion would do to him, Sherman runs off and joins the army of King Agamemnon in the Trojan Horse. During the final parts of the Trojan War, Penny is trapped inside the Horse as it rolls towards a cliff. Peabody rescues her, but apparently dies during the attempt.
Sherman pilots the WABAC to a few minutes before they left in the present to get Peabody’s help to fix everything. As Sherman and Penny try to explain the situation, Sherman’s earlier self shows up. Peabody tries to conceal the presence of two Shermans from the Petersons, then Grunion arrives. Then a second Peabody arrives from Ancient Troy. Grunion’s attempt to collect both Shermans causes them to touch and begin to merge. Both Peabodys rush to assist, but they each merge back together amidst a cosmic shockwave. Grunion grabs Sherman to take him away, hurting him. Peabody furiously bites Grunion, who then calls the NYPD. Peabody, Penny, and Sherman race to the WABAC, but cannot time travel due to a rip in the space-time continuum caused by the merger of their cosmic doubles. Historical figures and objects from the past begin falling from the cosmic rip and into the present.
Peabody crash-lands the WABAC in Grand Army Plaza at William Tecumseh Sherman’s statue’s base. Historical figures and police officers quickly surround them. Grunion calls in Animal Control to collect Peabody. Sherman explains that everything was his fault, but Grunion contends that it’s all because a dog can’t raise a boy. Sherman climatically shouts down Grunion, saying that if being a dog means being as loving and loyal as Peabody is, then he’s proud to be a dog too. Penny, her parents, the historical figures, and others all make the same pledge. George Washington is able to grant Peabody a presidential pardon which is supported by Abraham Lincoln and Bill Clinton.
Peabody, Leonardo da Vinci, Albert Einstein, Isaac Newton, and Agamemnon try to figure out how to close the rip, Sherman suggests they travel into the future. Peabody and Sherman take off in the WABAC and undo the damage. The historical figures are dragged back to the respective times, with Agamemnon abducting Grunion back to his own time as she vows revenge on Peabody.
Sherman returns to school having made friends with Penny. History meanwhile is contaminated with modern traits, while Grunion and Agamemnon get married in the Trojan Horse.