The film begins at a Russian space station where a cosmonaut is working outside, singing Frank Sinatra songs in Russian. A piece of space debris flies into the space station, spinning it out of control and sending the cosmonaut into deep space. The Russians are saved however, when Superman (Christopher Reeve) flies to the rescue, first putting the space station back into it's orbit and then rescuing the cosmonaut.
In Smallville, Superman aka. Clark Kent returns to the old Kent farm which is being put up for sale. In the barn, Clark listens to a message from his Kryptonian mother (Susannah York) which explains that the green crystal he holds is the very last source of Kryptonian energy and that he should use it wisely. At that point, a car arrives at the farm and Clark puts the crystal in his pocket.
A realtor named Hornsby (Don Fellows) greets Clark with the news that a big company wishes to buy the land unseen, much to Clark's dismay. Refusing to sell to anyone uninterested in the farm itself, Clark then returns to Metropolis. On the subway, Lois Lane (Margot Kidder) is practicing her French for an upcoming trip. Clark, just behind, misses the train and waits on the platform. The train driver suffers an apparent heart attack and causes the vehicle to pick up speed, hurtling past the next station. Clark hears the panic from the train and steps into a nearby phone booth, where he changes into Superman. Superman then flies past the train and gets ahead of it, stepping on the tracks to stop the train's power. While the emergency team attend to the driver, Superman informs the public that the subway is still the safest and most reliable form of transport and then flies away.
At the Daily Planet, Clark arrives to discover that a media mogul named David Warfield (Sam Wanamaker) and his daughter Lacy (Mariel Hemmingway) are to take over the newspaper, with plans to turn it into a sleazy tabloid. Clark's outspoken opinions on delivering the truth is noticed by Lacy who develops a liking for him. Meanwhile, Lois' trip is cancelled and editor Perry White (Jackie Cooper) heads off to the bank to try and get funds to buy back his newspaper.
Meanwhile, Lex Luthor (Gene Hackman) is broken out of jail yet again, this time by his young nephew Lenny (Jon Cryer) who Lex refers to as 'the dutch elm disease' of his family tree. His first plan on breaking out of prison is to destroy Superman and his first port of call is the museum where a strand of Superman's hair supports a massive ball of steel. After the museum closes, Lex steals the strand of hair.
Elsewhere, peace talks break down between the world's superpowers and the U.S. President (Robert Beatty) appears on TV to say that America 'strive to become second to none in the nuclear arms race'. A school boy named Jeremy (Damien McLawhorn) writes a letter to Superman, asking him do something about the crisis, and sends it to the Daily Planet.
Superman is moved by the letter but cannot intervene in global politics and when he seeks guidance from the Kryptonian elders (at the Fortress of Solitude), they encourage him to move on to another planet where war is forgotten. But Superman decides that Earth is his home and addresses the UN, with the world's press in attendance. He proposes to do what no one else can, or will, which is to 'rid the world of all nuclear weapons'. Following a tremendous applause, the superpowers all begin to launch their missiles into space where Superman collects them in a gigantic net. The net is sent flying into the sun by Superman, destroying the missiles safely.
At Lex Luthor's penthouse, a trio of arms dealers hear Luthor's plan to make a fortune re-arming the world and to get rid of Superman, which involves creating a clone with the same deadly powers. Using protoplasm grown from Superman's hair strand, Lex infiltrates a missile compound and attaches the protoplasm to the last remaining missile to be launched. Superman again catches the missile and throws it into the sun.
Immediately, a lifeform emerges from the fiery star and grows rapidly into a full grown man. Crackling with power, the 'Nuclear Man' (Mark Pillow) flies to Metropolis. Lex is impressed, not by Nuclear Man's power, but his own intelligence. Nuclear Man, however, has one major flaw - his power is drawn from the sun, and when he is not in direct sunlight he becomes incapacitated.
Meanwhile, at Lacy's apartment, Clark and Lois attend a double-date with Clark having to be both himself (who Lacy is attracted to) and Superman (who Lois still has feelings for). The dinner is interrupted when Lex transmits a supersonic message to Superman, leading him to his penthouse. Just after arriving, Superman is confronted by his new enemy, Nuclear Man. The pair become locked in battle, as Nuclear Man leads his enemy around the world, setting off a volcano in Italy and destroying the Great Wall of China. Finally, Nuclear Man takes the Statue of Liberty and drops it over Metropolis. Superman catches it just in time, but leaves him vulnerable to Nuclear Man who scratches him with his radioactive nails.
Superman, severely injured, manages to replace the Statue of Liberty but is kicked into sky, with only his cape left flapping in the wind. Presumed dead by everyone except Lois, Superman/Clark appears to be suffering some sort of rapid ageing and takes the green crystal that he pocketed earlier. With Superman out of the action, Lex begins raking in the money from his arms deals while Nuclear Man becomes obsessed with Lacy Warfield after seeing her picture.
On the streets of Metropolis, Nuclear Man wreaks havoc searching for Lacy. Through the smoke emerges a fully recovered Superman who lures him into an elevator and manages to cut off the sunlight, causing Nuclear Man to shut down. The Man of Steel flies the elevator into space and dumps it on the moon's surface. But a crack in the door allows Nuclear Man to catch the sun's rays, starting a fight on the lunar surface. During the battle, Superman is buried in the ground while Nuclear Man finds Lacy at the Daily Planet and flies her out towards deep space. Superman climbs out of the ground and manages to save Lacy by causing an eclipse, allowing him to then deal with Nuclear Man by dropping him into a nuclear reactor.
Back at the Daily Planet, Perry White has managed to secure funds at the bank and buys back control of the newspaper. Superman takes Lenny Luthor to a boys' home and his uncle back to prison, where the film ends.