The film opens in a narrative (Tony Jay
) which introduces us to deep space where merchant ships sail on solar winds transporting valuable cargo. However, their journeys are not without danger as one of them is attacked by a small pirate ship commanded by the notorious Captain Nathaniel Flint, a pirate who vanished without a trace after each heist and was rumored to have stashed his loot on the mysterious Treasure Planet. The image of Flint's alien face is soon seen to be a holographic image in the storybook of young Jim Hawkins (Austin Majors
), a three year-old boy who is completely immersed in the story. His mother, Sarah (Laurie Metcalf
), comes into Jim's room to put him to bed, playfully tackling him, but Jim continues to read his book, even under the covers. Twelve years later and Jim has grown into a strong teenager, taking thrills from solar surfing (windsurfing on a solar-powered rocket board), his favorite pastime. Unfortunately, the aloof Jim takes his board through a restricted construction zone and is quickly apprehended by authorities.
Meanwhile, back home at the Benbow Inn, Sarah tirelessly serves customers including the frequent dog-like Delbert Dopplar (David Hyde Pierce
), an astrophysicist and friend of the family. He asks how Jim has been doing just as Jim is brought home, flanked by two robotic police officers. They explain that if Jim performs any further transgressions he will be locked away in juvenile hall. Later that night, while Jim listens from the roof, Sarah confides in Delbert that, ever since his father left, Jim hasn't been the same. Despite being smart, he fails in school and acts distant. At that moment, Jim notices a spaceship fall from the sky and crash at the end of the Benbow docking platform. He runs out in time to help the injured pilot, an old, snaky creature named Billy Bones (Patrick McGoohan
). Jim assists him back to the inn as it begins to rain and make it through the front door before Billy collapses. Before Sarah and Delbert can do anything, Billy gives Jim a golden sphere and tells him to 'beware the cyborg' before expiring. Shortly after, the inn is raided by a gang of pirates and Sarah, Jim, and Delbert barely escape before the inn is burned to the ground. They seek refuge at Delbert's home where Jim discovers the minute mechanics of the sphere and activates it to reveal a holographic map of the galaxy. They discover that the map holds the key to finding Treasure Planet. Eager to make his mother proud and help rebuild the inn, Jim proposes to go find the Planet with Delbert's help, who is more than excited at the prospect of charting an expedition of discovery. Sarah is against the plan at first, but Delbert assures her that it may just be the right thing to help Jim sail straight.
Delbert commissions a ship and a crew out of Belfast, the 'harbor' of which resembles the size and shape of a crescent moon. He and Jim depart for the RLS Legacy where they greet the stony first mate, Mr. Arrow (Roscoe Lee Browne
), before meeting the stern and cat-like Captain Amelia (Emma Thompson
). The crew is a motley but seemingly obedient bunch and, as the ship sets sail, Jim is sent down to work in the galley for John Silver (Brian Murray
), a cyborg who Jim becomes immediately suspicious of. Silver introduces Jim to his pet amorphous blob named Morph (Dane A. Davis
) that can change into any shape, and to the notion of hard work. Resentful over his menial tasks, Jim picks the wrong side of crew member Scroop (Michael McShane
), a large, spidery alien with a temper quelled only by Mr. Arrow's reprimand and a quick glare from Silver. Silver berates Jim for not picking his fights wisely but the two soon begin a relationship out of mutual respect. Silver keeps Jim busy on board and grows impressed with his increasing work ethic. Along the journey, they eventually bond from a master and ward relationship to one near father and son, their experiences montaged to the song 'I'm Still Here'. The sequence features flashbacks from Jim's early life showing his father acting indifferent towards him as a child before finally leaving without warning during his pre-teens.
It is clear that they enjoy each other's company and Silver praises Jim's mechanical and piloting skills when he fixes one of the ship's solar skiffs and takes it for a spin. After they return to the ship, an explosion rings out as a nearby star goes supernova. Amelia takes the ship into evasive maneuvers and instructs Jim to secure all the crew's harnesses to the mainmast. Due to the turbulence, Silver nearly falls overboard but is saved by Jim. At this time, Delbert discovers that the supernova is devolving into a black hole and is pulling the ship back into its core. The black hole releases sonic waves which rattle the ship. Delbert tells Amelia that two more will follow before they are pulled into the hole and she comes up with a plan to ride the last wave out with the ship's engines at full thrust. The next wave sends Mr. Arrow overboard but he is saved by his harness line. However, Scroop appears above him and, with a sinister look, cuts his line, sending Arrow into the abyss. Silver and Jim hang on as the last wave erupts, sending the ship out of the black hole and back into deep space. Amelia addresses the crew and congratulates Jim and Delbert for their help before calling to Mr. Arrow. Scroop appears with Arrow's hat and claims his harness was not secure, to Jim's bewilderment. Scroop gives Silver a knowing glance, to Silver's disapproval. Jim takes the news, and Amelia's reaction, hard and retreats into seclusion. Silver finds him later and tries to pick him up again, telling him that he has the makings of greatness, if only he could see that himself and take charge of it. Jim's spirits are raised and he embraces Silver, much to Silver's surprise, before going below decks to sleep. Silver admits to Morph that he'd best watch how he acts around Jim, lest the crew thinks he's going soft.
The next morning, Jim is awoken early by a playful Morph. He chases him to the galley and catches him in a fruit barrel just before some of the crew comes down. Listening to their conversation, Jim learns that they're actually pirates that are planning a mutiny before they make land-fall. Silver comes into the galley, revealing himself as the mastermind and leader and expresses his discontent to anyone who makes a move before his say-so. Scroop tells Silver that he thinks Silver's gone soft for Jim and doesn't have it in him to continue with the plans. Enraged, Silver tells the crew that he cares only for Flint's treasure and that he warmed up to Jim to keep him ignorant to their plans. A cry comes from above that they've reached Treasure Planet, the exclamation coming from crewmember Onus (Corey Burton
), a six-eyed alien, and the crew leaves the galley. Jim emerges from the barrel and begins to make his way up to the deck but comes face to face with Silver on his way back down. They tensely stand off before Jim lunges forward with a pair of scissors and stabs Silver in his robotic leg, causing a pressure malfunction. Silver begins the mutiny as Jim retreats into Amelia's quarters and escapes with her and Delbert to the loading bay. However, ever-playful Morph grabs the map out of Jim's pocket, holding it in his mouth. Silver appears in the bay area and he and Jim try to coax Morph to go to them with the map. Confused, Morph dives into a bundle of ropes. Silver reaches for the map but Jim grabs it and escapes into the skiff with Amelia and Delbert. As they flee towards the planet's surface, Silver takes aim at them but refuses to shoot due to his attachment to Jim. However, a mutineer shoots the ship's cannon at the skiff, causing massive damage and injury to Amelia. The skiff crashes upside down on the surface.
The three compose themselves and Amelia asks for the map, but when Jim removes it from his pocket, it's revealed to be Morph in disguise. Jim realizes the map is still on the ship as a second skiff flies overhead, looking for them. Amelia orders Jim to find a safe haven for them before she collapses from her injuries. Delbert tends to the delerious Amelia while Jim scoures the alien jungle. He eventually comes into contact with a eccentric robot named B.E.N. (Martin Short
), short for Bio-Electronic Navigator. B.E.N.'s memory is hazy, at best, and he shows Jim that he's actually missing a part of his central database at the back of his head. Although, from what he does remember, he informs Jim that he was Flint's own navigator and was left on the planet to protect the treasure which is located at the 'centroid of the mechanism'. Jim is less than amused by B.E.N.'s antics but is relieved to find that B.E.N.'s lair is the perfect hiding place. Soon, however, the mutinous pirates surround the hovel and Silver demands the map. Knowing that Silver is unaware of the map's true location, Jim goes out to negotiate but refuses to cooperate with Silver. He returns to the hideout where B.E.N. reveals a 'back door' into a metal-works piping system that interweaves through the planet's very core. Jim, B.E.N., and Morph head back to the ship to deactivate the laser cannon and retrieve the real map while Delbert watches over Amelia.
On board, B.E.N. whimsically goes off to deactivate the cannon while Jim goes to the loading dock for the map. However, he runs into a vengeful Scroop and the two fight their way onto the main deck. B.E.N. accidentally deactivates the artificial gravity on the ship and Jim and Scroop float into the rigging. Jim is saved by grabbing onto the pirate's flag and, just before Scroop can cut him away, swings back onto the mast and kicks Scroop into the loose flag, sending him into space. B.E.N. turns the gravity back on and disables the cannon. When they return to the hideout, Jim holds out the map to Delbert only to see that Silver and the other pirates have invaded the place and tied Amelia and Delbert up. Jim is the only one who knows how to properly activate the map and thus demands that they all travel together to the treasure's location. They take the skiff and follow a laser trail to a cliff's edge where the trail disappears. An inscription on the ground reveals a plug for the map. Jim inserts it and a portal is engaged, with each planet's location on the map's hologram allowing for immediate travel; the secret to Flint's mysterious raids. Jim selects the Treasure Planet icon and the center of the planet is revealed with the treasure inside. Jim, the pirates, and B.E.N. step inside, walking through an unseen trip-laser. At the heart of the treasure, Jim discovers the remains of Captain Flint, clutching what seems to be the rest of B.E.N.'s 'mind'. Jim plugs it back into B.E.N.'s head and he suddenly remembers that Flint actually commissioned him to booby-trap the planet to make sure no one took his treasure. The very core begins to rip apart and scores of treasure, and some of the pirates, are lost in the molten center. Silver finds himself torn between collecting what treasure he can and saving Jim, hanging from a precarious ledge. Silver saves Jim and the survivors escape back to the Legacy as the planet begins to break apart. The ship becomes damaged and Amelia realizes that they'll never make it out of the planet's atmosphere in time. Jim comes up with a plan to activate the portal so that it takes them directly to Bristol. He attaches a rocket engine to a scrap of metal and surfs it ahead of the ship to the portal. Nearly failing, Jim manages to make it to the portal and enter in the coordinates, allowing himself and the ship to pass safely through just as Treasure Planet explodes.
Amelia orders the remaining pirates imprisoned in the ship's barracks as they return home and offers to recommend Jim to the Interstellar Academy for his actions. Later on, Silver sneaks down to the loading bay and sets off to escape in the skiff. Jim catches him in the act but lets him go. Morph decides to stay with Jim and Silver commends his bravery and predicts that he will 'rattle the stars'. He hands over a small fortune of treasure for Jim to rebuild the inn with, and leaves. The movie ends with the Benbow Inn rebuilt, B.E.N. providing waiter services for Sarah, and Delbert and Amelia married with children. Jim arrives home with two police officers, this time serving as escorts, as he reveals himself in a military cadet uniform. As everyone celebrates his home-coming, Jim looks to the skies and sees an approving image of Silver in the clouds.