Spider-Man (Nicholas Hammond) rescues a teenager-looking lady who tried to commit suicide by jumping off a skyscraper. At the The Daily Bugle Rita Conway (Chip Fields) is talking to Peter when somebody phones asking for a donation for some social cause from J. Jonah Jameson (Robert F. Simon) and they laugh it off, as Jonah is very tight and mean with money and salaries. He appears and tells Peter off because he didn't get a photo of Spidey. Rita defends Parker's good work performance and is not afraid of losing her job. He's not interested in Peter's idea for a news story.
At Miami Beach, a young editor called Sid (Simon Scott) sees the TV newscast about Spider-Man and sends a bitchy female journalist called Gale Hoffman (JoAnna Cameron) to get the exclusive about him. Her clue will be that Parker has been the only one close enough to Spider-Man to take a good picture of him.
At university, Dr ------------------- has put a reactor on college grounds. Peter Parker and three students disagree with the decision, and they think that anyone can create a nuclear bomb with it because of lack of security. The three other students decide to steal the reactor and create an atomic bomb to show everybody the dangers of nuclear power, and of putting anything nuclear at a low-security place. With the publicity, they hope to change the university's policy.
Gale interviews a specialist in spiders who sees the relation between spiders and Spidey's features. Peter is infatuated with Gale, who will tag along with Peter until Spidey appears. Peter feels the theft and goes after the three students and says goodbye to Gale alleging that he's got to see his tutor.
In Gstaad, Switzerland, a powerful man called Mr. White (Robert Alda) reads the news of the nuclear theft. He is no fool, and thinks that there were the students and not Spidey who robbed the university. The security guards do not see the noisy thee students, but they see Spidey, who appears on the outer wall of the premises to try to stop the burglary. Gale feels cheated by Peter when she sees the police coming while she is waiting for Peter at a café. The three students have put the plutonium within a led container. The newspaper says the plutonium is not dangerous, so Craig (Randy Powell) decides that the only way to make their point clear is to make their own nuclear bomb.
Mr White leads a lavish and luxurious life. He and Angel (Lawrence P. Casey), his henchman, fly to the USA. White can do karate.
It's Carla Wilson (Anne Bloom), who masters the plutonium. Gale pressures Peters to explain why he believes Spider-Man is not a thief. Peter defends the idea of responsibility: great power becomes great responsibility. Gale thinks that Peter wants to have Spidey's powers.
White calls Peter and tells him to call on him at the Plaza Hotel and Gale tags along.
Captain Barbera (Michael Pataki) has not made any progress to the case, and Inspector DeCarlo (Sidney Clute) is worried about that. DeCarlo blames Parker, although Barbera thinks it's unlikely.
White and Angel capture Peter and Gale as they think that he has the plutonium to blow up the World Trade Centre, but they run away. They walk on the cornice of the hotel and they escape down the fire stairs. They take a taxi and the diver (Barry Roberts) takes them to another hotel, as they realise they can't go home. Barbera and DeCarlo talk to Peter - he says that he slept at Gale's couch. The police think that Peter told Spidey where the find the plutonium, and they take him with them, although they don't have any proof.
Jameson tells Parker off and fires him. Gale tries to defend him to no avail. Peter has to hand in his press pass. Rita bangs the door. Ted (Steven Anderson) finishes the bomb. Carla feels terrible and they take her to hospital with radiation poisoning. Peter refuses Gale's sympathy. A doctor (Bonnie Johns) doesn't know if Carla will survive, and tells the other two students that she has to report the case. Rita gets wind of this and phones Peter Parker to tell him. Peter tells the other two students off - they had already talked at university. Angel eavesdrop all the conversation. Gale appears to give Peter some news but Peter wants to get rid of her. He goes onto the men's toilet room to change into his Spidey costume and then leaves through the window. When Gale enters, Peter is not there.
But Angel had phones Mr White and they get hold of the bomb first. In the ensuing fight, Spidey is hurled off a twelve story building and plunges to his death. However, he manages to save himself by creating a cushion net with his webbing. Later, Peter interrogates Ted and Craig, now in jail. DeCarlo and Barrera are worried and without a plan, and Peter says that exploding a bomb is easily done.
Peter admits to Gale that he left out of the window in order to meet Spidey. Rita gives more information about a license number.
At an LA mansion, the car Angel is driving has a transmitter from Spidey. Jameson talks to Peter and Gale again. Jonah doesn't want to pay the expenses to California. Jonah can't print the atomic bomb story or it will spread the panic, but the exclusive after they bomb has been depleted will give him the biggest exclusive of the century. Jonah wants to go with Parker to protect his 3,000 dollar investment, and Gale is also going to LA.
Gale sunbathes in LA, and Jonah does the same in his full suit clothes. Gale sees the transmitter, and Parker says it belongs to Spider-Man. Gale suspects him of being Spidey, but he rejects the notion. Peter admits that he's in the very same hotel. Following the signal, Jonah's car gets a flat tyre and Peter hires a motorbike; Gale followsuits, and tells the seller (Ron Hajak) that Jonah will pay everything. Jonah hires a kind of mower. Angel tries to lose Peter, and they reach a kind of ghost neighbourhood - it looks like a western town. Angel and a karate thug (Emil Farkas) will have a duel. Gale interrupts them but Spidey tells her to run away. After the duel, Angel runs away and he's lost the transmitter.
Rita tells Jameson that Mr. White demands $1,000,000,000 in return for not setting off the plutonium bomb in the place where "it can do the most damage". Gale thinks White means New York, but Peter realises it's the President of the USA's visit to LA where the most people will gather.
Peter and Gale go to a music studio where David Somerville and Gail Jensen are singing. Angel and the karate thug kidnap Gale and tie her down. They dress her in a bikini - White likes girls in bikinis and she won't have any place to hide any weapons. White admits to her that his plan is in LA, at a Governor conference, not in NY.
Spider-Man finally arrives to White's mansion and learns of White's plans. He fights against Angel again and leaves him hanging in a net. Gale confirms that downtown LA is in danger and that it's too late for the police to do anything. White is disguised as a maintenance man and he'll set it off if he's not paid ransom. Spidey goes with a helicopter driver (Walt Davis). So as not to make the pilot lose his license, he jumps from the copter to a particular roof where he's seen something strange. He shoots his web and holds to White's helicopter.
White leaves, leaving the bomb behind. The countdown goes on. Spidey deactivates it taking out the right wire only two seconds before time. White has run away, but he tells the pilot that in spite of his plan having gone awry, he is not unhappy because he knows he'll meet Spider-Man soon enough.
Gale still thinks that Peter is Spider-Man; Peter denies it and they flirt when Jameson is out of the way.