In 1962, Burt Munro is a sort of folk hero in his home town of Invercargill, New Zealand, known for his friendly easy-going personality, for having the fastest motorcycle in New Zealand and Australia, and for being featured in Popular Mechanics magazine. However, that recognition is contrasted by his exasperated next-door neighbours, some of whom are fed up with his un-neighbourly habits; such as revving his motorbike early in the morning, urinating on his lemon tree, and not mowing his grass. Burt, however, has a long-time dream; to travel to the US and test his motorbike’s capabilities at the Bonneville Speedway.
Burt is finally able to save enough to travel by cargo ship to Los Angeles, but when he arrives, he experiences bureaucracy, skepticism, and the indifference of big city people. It is his blunt but gregarious nature which overcomes each hurdle. He wins over the motel clerk, a transgender woman named Tina, who assists him in clearing customs and helps him in buying a car. The car salesman allows Burt to use his workshop and junkyard to build a trailer, and later offers him a job after Burt fine-tunes a number of the cars on the lot. Burt declines the offer, however, and shortly afterwards begins his long trip to Utah.
Along the way, Burt meets numerous helpful people, including highway police, a Native American who aids him when his trailer fails, a woman named Ada who allows him to repair his trailer and briefly becomes his lover, and an Air Force pilot who is on leave from military service in Vietnam.
He finally arrives at the Bonneville Salt Flats, only to be blocked by race officials for not registering his motorcycle for competition in advance, and not having the mandated safety equipment. In a show of sportsmanship, however, various competitors and fans in the Bonneville series intervene on his behalf, and he is eventually allowed to make a timed run. Despite various problems, he succeeds in his quest and sets a new land speed record at the 8th mile of his run; when he reaches 201.851 mph (324.847 km/h). By the end, his leg is burned by the exhaust, and he then falls with the motorcycle and skids to a stop, but he is able to return home to New Zealand a hero.