In 1938, Cliff and mechanic A. "Peevy" Peabody find a mysterious rocket pack inside a biplane of their employer's hangar. Cliff experiments with it, but Peevy persuades him to leave the rocket alone until he can understand its design and fine-tune it.
Shortly afterwards, at an airshow, Cliff uses the rocket (with Peevy's newly designed, face-hiding helmet) to heroically rescue his elderly friend Malcolm piloting a malfunctioned aircraft. Having been seen by the audience, a media sensation ensues, and Cliff, as the anonymous hero, is dubbed "the Rocketeer". However, Cliff and his aspiring actress girlfriend, Jenny Blake, begin to have relationship issues after Cliff visits her on-set of a film and inadvertently causes an accident. Jenny is fired over Cliff's accident; however, Neville Sinclair, who is portraying the lead role of the production, overhears Cliff's attempt to tell Jenny about the rocket pack. After Cliff leaves, Sinclair makes up to Jenny and invites her to dinner at the famed South Seas Club. Sinclair then sends his assistant, Lothar, to search the airfield for Cliff.
Cliff consults with Peevy in their shared home, where Lothar attacks and seizes detailed rocket pack schematics drawn up by Peevy, but they are interrupted by the arrival of the FBI. Cliff and Peevy escape with the rocket. Cliff and Peevy arrive at the local diner but are trapped by a team of mobsters who are searching for Cliff, but don't recognize him. Overhearing them consult with Eddie over the diner's phone, Cliff learns of Jenny's date with Sinclair and the latter's involvement with the crime. The diner patrons overpower the mobsters, but a stray ricochet punctures the rocket pack's fuel tank, which Peevy provisionally patches with Cliff's chewing gum. Cliff proceeds to and infiltrates the South Seas Club but is nearly trapped by Valentine's gang, and in the ensuing melée, Jenny is kidnapped by Sinclair.
Sinclair tries to seduce Jenny at his villa, but she knocks him out and, trying to escape, discovers that he is a spy. Sinclair recaptures her with Lothar's aid and leaves a message for Cliff: bring the rocket pack to the Griffith Observatory that very night in exchange for Jenny's life. Cliff hides the rocket just before he is arrested by the FBI, who take him to Hughes. Hughes reveals that the rocket, called the Cirrus X-3, was a prototype similar to one Nazi scientists were unsuccessfully developing to invade the United States (as shown in a propaganda film the FBI show Cliff that was smuggled out of Nazi Germany). When Hughes demands the return of the rocket, Cliff explains that he needs it to rescue Jenny; when the FBI protests, Cliff escapes, but inadvertently leaves behind a clue to the location of the exchange.
Recostumed as the Rocketeer, Cliff flies to the rendezvous where Sinclair, Lothar and the Valentine gang are waiting. When Sinclair demands the rocket, Cliff divulges to the gang that the actor is a Nazi spy. Eddie, drawing the line at treason, turns on Sinclair, but Sinclair unexpectedly summons Nazi SA commandos hidden nearby and the gang are held at gunpoint as a Nazi Zeppelin, the Luxembourg, touring America in a "gesture of friendship" but actually secretly assisting the mission, appears overhead. A fight ensues between the Nazis and the FBI agents who have followed Cliff, as well as Eddie and his men, but Sinclair and Lothar escape with Jenny aboard the Zeppelin. Cliff uses the rocket to reach and board the Zeppelin, but during the ensuing showdown Jenny accidentally sets the craft on fire with a flare gun. Sinclair takes the rocket to save himself, but not before Cliff thumbs off the chewing gum patch; with the leaking fuel ignited by the exhaust flame, Sinclair dies crashing down upon the last four giant letters of the "Hollywoodland" sign. Lothar is engulfed in flames as the Zeppelin explodes, but Cliff and Jenny are rescued at the last instant by Hughes and Peevy in an autogyro.
Some time afterwards, Hughes presents Cliff with a brand-new Gee Bee racing aircraft as a compensation for the one he lost at the start of the adventure. As Hughes leaves, Jenny presents Peabody with the rocket blueprints she found in Sinclair's villa. Peabody decides that with some modifications, he can build an even better one.
- Howard Hughes: "How did it feel, strapping that thing to your back and flying like a bat out of hell?"
- Cliff Secord: (awed) "Well, it's the closest I'll ever get to heaven." (looking over at Jenny)
- Cliff Secord: "Well, maybe not."
- After Cliff puts on the rudder helmet so he can steer/control the rocket, he is frequently seen turning his head without changing his course or direction.