In 1912 Houston, as eight-year-old Howard Hughes’ mother gives him a bath and teaches him how to spell “quarantine”, she warns him about the recent cholera outbreak in Houston: “You are not safe.” Fourteen years later, in 1927, he begins to direct his film Hell’s Angels, and hires Noah Dietrich to manage the day-to-day operations of his business empire. After the release of The Jazz Singer, the first partially talking film, Hughes becomes obsessed with shooting his film realistically, and decides to convert the movie to a sound film. Despite the film being a hit, Hughes remains unsatisfied with the end result and orders the film to be recut after its Hollywood premiere. He becomes romantically involved with actress Katharine Hepburn, who helps to ease the symptoms of his worsening obsessive-compulsive disorder (OCD).
In 1935, Hughes test flies the H-1 Racer, pushing it to a new speed record, despite having to crash-land into a beet field when the aircraft runs out of fuel. Three years later, he breaks the world record by flying around the world in four days. He subsequently purchases majority interest in Transcontinental & Western Air (TWA). Juan Trippe, company rival and chairman of Pan American World Airways (Pan Am), gets his crony, Senator Owen Brewster, to introduce the Community Airline Bill, which would give Pan Am exclusivity on international air travel. Hepburn grows tired of Hughes’ eccentricity, and leaves him for fellow actor Spencer Tracy. Hughes quickly finds a new love interest with 15-year-old Faith Domergue, and later actress Ava Gardner. However, he still has feelings for Hepburn, and bribes a reporter to keep reports about her and the married Tracy out of the press.
In the mid 1940s, Hughes contracts two projects with the Army Air Forces, one for a spy aircraft, and another for a troop transport unit for use in World War II. In 1947, with the H-4 Hercules flying boat still in construction, Hughes finishes the XF-11 reconnaissance aircraft and takes it for a test flight. However, one of the engines fails midflight, and the aircraft crashes in Beverly Hills, with Hughes getting severely injured. The army cancels its order for the H-4 Hercules, although Hughes still continues the development with his own money. Dietrich informs Hughes that he must choose between funding the airlines or his “flying boat”. Hughes orders Dietrich to mortgage the TWA assets so he can continue the development.
As his OCD worsens, Hughes becomes increasingly paranoid, planting microphones and tapping Gardner’s phone lines to keep track of her, until she kicks him out of her house. The FBI searches his home for incriminating evidence of war profiteering, searching his possessions and, to his horror, tracking dirt through his house. Brewster privately offers to drop the charges if Hughes sells TWA to Trippe, but Hughes refuses. Hughes’ OCD symptoms become extreme, and he retreats into an isolated “germ-free zone” for three months. Trippe has Brewster summon him for a Senate investigation, certain that Hughes will not show up. Gardner visits him and personally grooms and dresses him in preparation for the hearing. He asks her to marry him, and she just laughs and says that he is “too crazy” for her.
An invigorated Hughes defends himself against Brewster’s charges and accuses the senator of taking bribes from Trippe. Hughes concludes by announcing that he has committed to completing the H-4 aircraft, and that he will leave the country if he cannot get it to fly. Brewster’s bill is promptly defeated. After successfully flying the aircraft, Hughes speaks with Dietrich and his engineer, Glenn Odekirk, about a new jetliner for TWA. However, he begins hallucinating men in germ-resistant suits, and has a panic attack. As Odekirk hides him in a restroom while Dietrich fetches a doctor, Hughes begins to have flashbacks of his childhood, his love for aviation and his ambition for success, compulsively repeating the phrase, “the way of the future”.