The movie takes place in Los Angeles in the year 1938. At an airfield, a flight crew is moving a new plane (the GeeBee) out onto the runway. The pilot, Cliff Secord (Bill Campbell) is discussing the plane with his mechanic and best friend, Peevy (Alan Arkin). Cliff and Peevy intend to use the GeeBee in a national air show within a year. Cliff sticks a piece of Beeman's chewing gum on the wing of the plane for good luck and takes off to test out the GeeBee.
Meanwhile, a duo of gangsters are engaged in a gun fight with members of the FBI. Cliff flies overhead and the gangster (thinking Cliff may be law enforcement) shoots at the GeeBee. Cliff's engine begins to stutter as he maneuvers back towards the runway.
The gangsters arrive at the same runway and hide in a hanger. The driver, Wilmer, learns that the gunman has been fatally wounded in the shootout. Wilmer hides the package the 2 of them had stolen and heads back out into the fight. Cliff's GeeBee bumps into a car on the runway, crash landing. THe mechanic crew gets Cliff out alive, but he quickly rushes back in to retrieve a photo of his girlfriend. The GeeBee is totaled, and Wilmer crashes his car into a fuel truck, causing an explosion.
The FBI refuses to admit responsibility for Cliff's crash. They question Wilbur about the stolen package, who merely responds that it is "blown to Hell." They find a metal device in the wreckage of the fuel tank, and they assume this is the device in question. They report this to the owner, Howard Hughes (Terry O'Quinn) who is upset but decides not to build another device because the theft proves the technology too dangerous.
Cliff and Peevy argue with the owner of the air field, Bigelow (Jon Polito) who is holding them responsible for the damage to the fuel truck. He talks them into doing a pitiful "Clown Act" at his annual air shows, which Peevy calculates would result in taking a minimum of four years to settle their debt.
Cliff decides to work on the biplane they will be using for the Clown Act, putting his girlfriend's photo in the cockpit. He tries to sit down but finds something hidden under the seat. It is the package from the gangsters (hidden earlier to avoid detection). They open it to reveal a strange metal contraption. Cliff notices a switch on the side and presses it. The device roars to life and rockets round the room, finally crashing into an office. They quickly shut it off again, and Peevy wonders what such a device could be for. Cliff, noticing some straps on the metal, gets an idea. He picks up the item and attaches it to his back. Both men are shocked: the item is a rocket pack.
They steal a statue of Charles Lindberg from the local flight school and test it. They confrom that a person could, theoretically, fly with such an item. Cliff wants to use it to make money, but Peevy doesn't think its a good itea (since they have technically stolen this item). Peevy relents, and Cliff suggests they make a helmet to go with it after seeing the head of the statue destroyed because of the landing.
The leader of the gangsters, Eddie Valentine (Paul Sorvino) confronts the man who hired him- Neville Sinclair (Timothy Dalton)- about the job gone wrong. Neville is anxious to get the rocket package, and contacts his enforcer Lothar (Tiny Ron), ordering him to confront Wilmer in the hospital and find the package's location.
Cliff then goes to pick up his girlfriend, Jenny Blake (Jennifer Connelly). Jenny is an aspiring actress who recently tried out for a part with Neville Sinclair. She then tells Cliff that she wants to see Sinclair's newest movie. Cliff is against it, until he finds out that it is an aviation movie called "Wings of Honor." En route to the theater, Cliff lies to Jenny about the GeeBee test flight, stating that it wnt fine except for "a few bumps" on the landing.
At the hospital, Lothar (revealed to be a gigantic physical specimen) confronts Wilmer. Wilmer confesses that he put a fake package in the car before it blew up, concealing it from the Feds. He tells Lothar the package is in an old plane at the airfield. Lothar then proceeds to kill WIlmer by literally folding him in half.
After the movie, Cliff and Jenny have dinner at a local restaurant called the Bulldog Cafe. Cliff's old friend Malcolm (Eddie Jones) reveals the truth about what happened during the test flight. Angry that Cliff lied to her, Jenny storms out.
Cliff returns home to the place he rents with Peevy and finds the helmet Peevy designed for him next morning. He is not thrilled with the design.
Next day, Jenny is performing in a scene as an extra on Neville Sinclair's new movie. Cliff comes by to see her (having decided to be honest with her and tell her about the rocket) and accidentally knocks down part of the set. Outraged, Neville orders Jenny fired. She is devastated and walks off. Neville overhears Cliff talking to Jenny about the rocket and decides to find out what she knows. Neville invites Jenny to be his date to the South Seas Club that night. She happily accepts.
At the air field, the stunt show is in process. Bigelow tells Peevy that if Cliff doesn't arrive soon and begin the Clown Act, they will both be fired. Malcolm, selling programs, overhears this and sees a way to help out his friend. Malcolm takes the costume and lifts off in the old biplane.
Eddie Valentine and his gang are at the airfield. They did not find the rocket, but took the picture of Jenny that Cliff left in the plane, thinking she may know who took the package.
Cliff and Peevy realize what Malcolm is doing and are worried (Malcolm hasn't flown a plane in over 20 years). The biplane begins to stutter and smoke billows from the engine. Cliff decides to take the rocket and save Malcolm. Peevy is hesitant, but lets his friend go (first grabbing a piece of Cliff's Beeman Gum and sticking it to the rocket pack for luck). Cliff blasts off in the rocket, flying over the stands and stunning the crowd. He grabs Malcolm shortly before the biplane crashes and safely drops his friend off on the ground before blasting off again.
Cliff flies over the city, passing a commercial plane in the process. He waves at them, but in the process accidentally shuts off the rocket. He falls to earth but manages to turn the thrusters back on again, speeding off in a disoriented pattern. Peevy finally finds Cliff after he's crash-landed in a nearby pond. Cliff is dazed, but thrilled by the experience. They both see cars coming, thinking it is news reporters. Cliff uses the rocket pack when standing in Peevy's truck to help them make a speedy getaway. In truth, the cars belonged to Valentie's gang and they are angry that someone else has found the rocket.
Reporters question Bigelow for information about the flying man, and he comes up with the name "Rocketeer" for him. The news boys love it and The Rocketeer is soon front-page news. Neville Sinclair reads the paper and is outraged. Howard Hughes also sees the paper and is upset that the FBI have failed in reclaiming his rocket.
The FBI agents go to talk to Bigelow about the Rocketeer, only to find him murdered in a matter similar to Wilmer. Before he died, Bigelow wrote down something on a pad of paper. It turns out to be Cliff & Peevy's addres, which is where Lothar is heading.
Lothar confronts Peevy and Cliff about the rocket, which they have hidden. The FBI arrive to question them as well and Lothar opens fire on the agents. The ensuing gunfire tears the house to shreds, but Cliff & Peevy manage to escape with the rocket.
Jenny and Neville are at the South Seas Club, and Jenny is enjoying being Neville's date. She meets a number of his celebrity friends, including W.C. Fields. Neville excuses himself to have a meeting with the Clubs' owner, which turns out to be Eddie Valentine. Eddie is not happy about Wilmer's death, or about Neville "romancing some dame" while he is doing all the hard work looking for the rocket.
Cliff and Peevy are hiding out above the Bulldog Cafe. Peevy finally convinces Cliff to return the rocket pack to its rightful owners. Cliff is about to call the local FBI office when 2 of Valentine's thugs come in. They demand to know where Secord is (having no idea what Cliff looks like), going so far as to torture Peevy for information. One of them recognizes a photo of Jenny on the wall as being identical to the one they recovered from the plane. They call the number associated with the photo and find out that Jenny is out with Neville Sinclair.
Cliff and a few of the patrons attack the gun-wielding thug, knocking him out cold. Cliff puts on the rocket, worried about Jenny's safety and intending to rescue her. He vows to return the rocket as soon as Jenny is safe. Peevy stops him from blasting off, noticing that the rocket is leaking (probably from a ricochet bullet). Peevy pries off the chewing gum he put on the rocket earlier for luck, and makes a rudimentary patch. It appears to work, and Cliff flies off into the night.
Cliff infiltrates the South Seas Club posing as a busboy, bringing some complimentary soup to Neville and Jenny. He "accidentally" spills some on her to get her away from Neville. Cliff tells Jenny that his boss Bigelow is dead and the people who killed him may also be after Jenny. He asks Jenny to leave and stay with her mother north of town for the next few days. Jenny is skeptical, but Cliff swears that he is looking out for her best interest and not motivaded by jealousy.
The thugs recognize Secord and chase after him. Cliff reclaims the rocket he had kept hidden in the laundry room. The Rocketeer flies out over the main room of the club, stunning the guests. Jenny stays for a moment to watch Cliff fly. The thugs open fire, heavily damaging the club. Cliff manages to escape by flying through the glass tile roof. Neville sees Jenny still at the club and ambushes her with chloroform.
Jenny wakes up at Neville's place. He claims innocence, saying that he is being blackmailed. Jenny doesn't believe him, realizing that Sinclair is merely reciting lines from his old movies in an attempt to gain her trust. Jenny knocks out Sinclair with a flower vase and runs off. She discoveres a secret room in his house full of radio equipment. She attempts to call for help, but only heres men speaking in German. She then notices a book with a swastika symbol and Jenny realizes that Neville Sinclair is a Nazi spy. Lothar attacks Jenny and subdues her.
Cliff returns to the Bulldog Cafe to find Peevy gone. He gets a phone call from Eddie Valentine saying that they are holding Jenny hostage and wish to trade her for the rocket. They tell Cliff to come to the local observatory at 4 AM to carry out the deal. Before Cliff can react, the FBI agents come in and arrest him.
The FBI agents bring Cliff to Howard Hughes, which is where Peevy went. Peevy told Hughes everything about their finding the rocket, and Hughes believes they are telling the truth. Hughes tells Cliff that the rocket pack was stolen from his factory and they must get it back. Hughes shows footage of German scientists working on a similar rocket pack, but their model backfires and the test pilot is killed. He then shows everyone a Nazi propaganda film that features rocket-pack equipped soldiers flying out to other countries (including the United States) as an unstoppable airborne army.
Cliff does not relent, and requests that he use the rocket once more in order to save his girlfriend. The FBI agents tell him that the Valentine Gang is merely hired muscle, working for a Nazi agent they haven't been able to identify. Cliff realizes that Neville Sinclair must be the agent, but the FBI just laughs at the thought. Cliff escapes from Howard Hughes' factory by gliding on a prototype "Spruce Goose."
The Rocketeer meets up with Neville Sinclair and the Valentine gang at the observatory. They demand he take off the rocket before they let Jenny go. Cliff asks Valentine if he enjoys working for a Nazi. Valentine is shocked, but Sinclair merely laughs off the thought. Jenny supports Cliff's claim by mentioning the Germans on the radio at Sinclair's house. Valentine is disgusted by the thought of working on the side of the Nazi's, and turns on Sinclair. Sinclair has prepared for this, and by his orders a team of German Strike Commandoes emerge from the bushes. They are supported by a Zeppelin, which hovers ominously over the observatory.
Searchlights flare up over the site. The FBI, having found the ransom details among Cliff's possessions, order everyone to throw down their weapons. The Germans try to evacuate, so the Feds and the gangsters unanimously open fire on the Germans. They warn each other to keep the fire away from the Zeppelin, which is full of hydrogen gas and highly explosive.
Neville takes Jenny hostage aboard the Zeppelin, certain that Cliff (and the rocket) will then come right to him. Cliff grabs a weapon from a fallen German commando and blasts off towards the Zeppelin. He tears through the covering on the tail section, damaging their steering. Lothar attacks Cliff on top of the Zeppelin, held up by a suspension cord. Cliff manages to knock Lothar over the side, where he dangles like a worm on a hook.
Cliff comes inside and sees Neville holding a gun to Jenny's head. Seeing no other choice, he takes off the rocket. Before he slides it over to Neville, Cliff removes the patch Peevy put over the bullet hole (which Neville doesn't notice.)
Cliff and Neville struggle, and Jenny tries to assist with a gun she found in the storage compartment. Cliff warns her against it but Jenny fires- not realizing that the item was a flare gun. Fire breaks out in the cockpit, and Neville Sinclair decides to fly off in the rocket. Moments after he takes flight, the leak from the fuel line causes Sinclair to burst into flames. Screaming in pain, he crashes into the legendary "Hollywoodland" sign, destroying the last four letters. Neville and the rocket are destroyed.
Cliff climbs back up to the top of the Zeppelin with Jenny, explaining that they have almost no hope for survival. Jenny proclaims that she loves Cliff, and they embrace. Lothar returns to fight Cliff again, but the explosions from the Zeppelin cause all 3 to run in fear. Lothar is still held in place from his tether and cannot escape the blast.
Peevy and Howard Hughes fly up in Hughes' prototype auto-gyro, dangling a rope ladder for Clifford and Jenny. They escape shortly before the Zeppelin is engulfed in flames.
Next morning, Peevy reads the newspaper. The FBI has decided to cover up Neville Sinclair's Nazi involvement, releasing a cover story that Sinclair was killed by debris from the Zepplin in a tragic accident.
Cliff, Peevy and Jenny go outside to see a small plane (in similar design ot the GeeBee from the opening) landing in the street. Howard Hughes is the one flying the plane, and he takes Cliff aside and reveals that this plane is a gift hor helping him with the rocket fiasco.
Cliff is so stunned that he cannot even thank Howard Hughes. Jenny s states that she also has a gift- for both of them. Jenny reveals that she stole teh schematics for the rocket pack from Neville Sinclair's house. Cliff and Jenny enjoy a romantic moment while Peevy plans to rebuild the rocket pack with a variety of improvements.