In the New Zealand town of Invercargill, Burt Munro (ANTHONY HOPKINS) is known as something of an eccentric old man with a penchant for peeing on his lemon tree and racing his 1920 Indian Spirit motorcycle at high races down the beach. While his neighbors aren't fond of his behavior, he has a fan in the form of their son Tom (AARON MURPHY) who helps Burt in his backyard shed. Despite his bike being more than 40 years old, Burt can out-race anyone with it, although he goes to unorthodox means to keep it running.
His big dream is taking it to the legendary Bonneville Salt Flats in Utah and seeing if he and his bike can break the land speed record. Unfortunately, while he might have the support of Tom as well as his new friend Fran (ANNIE WHITTLE), Burt is short of the funds necessary to travel to the States, get a car and enter his bike into the prestigious Speed Week competition.
With a bit of ingenuity, however, he gets himself on a ship and lands in Los Angeles where a number of locals -- including transvestite motel clerk Tina (CHRIS WILLIAMS) and used car salesman Fernando (PAUL RODRIGUEZ) -- assist him in various ways, including dealing with his good-natured naiveté about America. As he makes his way from L.A. to Utah, he meets more people -- such as American Indian Jake (SAGINAW GRANT), the friendly and amorous widow Ada (DIANE LADD) and finally fellow racer Jim (CHRIS LAWFORD) -- who similarly help him on his quest.
When he finally arrives at the salt flats, he must overcome additional obstacles and challenges as he prepares to see if he and his bike have what it takes.