Detroit engineer Preston Tucker (Jeff Bridges) has been interested in building cars since childhood. During World War II he designed an armored car for the military and made money building gun turrets for aircraft in a small shop next to his home in Ypsilanti, Michigan. Tucker is supported by his large, extended family, including wife Vera (Joan Allen) and eldest son Preston Jr (Christian Slater).
As the war winds down, Tucker has a dream of finally building the "car of the future." The "Tucker Torpedo" will feature revolutionary safety designs including disc brakes, seat belts, a pop out windshield, and head lights which swivel when you turn. Tucker hires young designer Alex Tremulis (Elias Koteas) to help with the design and enlists New York financier Abe Karatz (Martin Landau), to arrange financial support. Raising the money through a stock issue, Tucker and Karatz acquire the enormous Dodge Chicago Plant to begin manufacturing. Abe hires Robert Bennington (Dean Goodman) to run the new Tucker Corporation on a day to day basis.
Launching "the car of tomorrow" in a spectacular way, the Tucker Corporation is met with enthusiasm from shareholders and the general public. However, the Tucker company board of directors, unsure of his ability to overcome the technical and financial obstacles ahead, send Tucker off on a publicity campaign, and attempt to take complete control of the company. While Tucker travels the country, Bennington and directors change the design of Tucker's car to a more conventional design, eliminating the safety and engineering advances Tucker was advertising. At the same time, Tucker faces animosity from the Big Three and the authorities led by Michigan Senator Homer S. Ferguson (Lloyd Bridges).
Tucker returns from his publicity tour and confronts Bennington, who curtly informs him that he no longer has any power in the company to make decisions, and the engine originally planned for the car is not viable. Tucker then receives a call from Howard Hughes (Dean Stockwell), who sends a private plane to bring Tucker to his aircraft manufacturing site. Hughes advises Tucker to purchase Air Cooled Motors, which can supply both the steel Tucker needs, as well as a small, powerful helicopter engine that might replace Tucker's original "589" power plant.
Faced with being unable to change Bennington's design, Tucker modifies the new engine and installs it in a test Tucker in the secrecy of his backyard tool and die shop. This prototype proves successful in both durability and crash testing. However, Tucker is confronted with allegations of stock fraud. Ferguson's investigation with the U.S. Securities and Exchange Commission (SEC), causes Karatz, once convicted of bank fraud, to resign, fearful that his criminal record will prejudice the hearings. Yellow journalism starts ruining Tucker's public image even though the ultimate courtroom battle is resolved when he parades his entire production run of 51 Tucker Torpedoes, proving that he has reached production status.
After giving a speech to the jurors on how capitalism in the United States is harmed by efforts of large corporations against small entrepreneurs like himself, Tucker is acquitted on all charges. Nevertheless, his company falls into bankruptcy and Preston Tucker succumbs to a heart attack seven years later, never able to realize his dream of producing a state-of-the-art automobile.
The film ends with all 51 Tucker Sedans being driven down the streets of downtown Chicago, admired by everyone as they pass.