Young journalist Tintin and his dog Snowy are browsing in an outdoor market in London, England. Tintin buys a miniature model of a ship, the Unicorn, but is then accosted by Barnaby and Ivan Ivanovitch Sakharine, who both unsuccessfully try to buy the model from Tintin. Tintin takes the ship home, but it is accidentally broken, resulting in a parchment scroll slipping out of the model and rolling under a piece of furniture. Meanwhile, detectives Thomson and Thompson are on the trail of a pickpocket, Aristides Silk. Tintin later finds the “Unicorn” model is stolen and his apartment ransacked. He visits Sakharine in Marlinspike Hall and accuses him of the theft when he sees a miniature model of the “Unicorn”, but when he notices that Sakharine’s model is not broken, he realizes that there are two “Unicorn” models. Once Tintin returns home, Snowy shows him the scroll. After reading an old message written on it, he is interrupted by the arrival of Barnaby, who is fatally shot and killed unquestionably. Tintin places the scroll in his wallet, but it is stolen by Silk the next morning.
Later, Tintin is abducted by accomplices of Sakharine and imprisoned on the SS “Karaboudjan”. He learns that Sakharine formed an alliance with the ship’s staff and led a mutiny to take over control. On board, Tintin meets Captain Haddock, the ship’s nominal captain. Haddock is permanently drunk and thus unaware of the happenings on board his ship. Tintin, Haddock, and Snowy eventually escape from the “Karaboudjan” in a lifeboat but the ship’s crew tries to ram it. Presuming them to have survived, Sakharine sends a seaplane to find them, which the trio seize and use to fly towards the fictitious Moroccan port of Bagghar. The seaplane soon crashes into the desert, due to low fuel.
While trekking through the desert, Haddock hallucinates and remembers facts about an ancestor of his, Sir Francis Haddock, who was a 17th-century captain of the “Unicorn”. Sir Francis’ treasure-laden ship was attacked by the crew of a pirate ship, led by Red Rackham. After defeating Red Rackham, Sir Francis sank the “Unicorn” and most of the treasure to prevent it from falling into Rackham’s hands. Sir Francis prepares three “Unicorn” models, each containing a scroll; together, the scrolls can reveal coordinates to the location of the sunken Unicorn and its treasure.
The third model is in Bagghar, possessed by Omar ben Salaad. In a concert by opera diva Bianca Castafiore, Sakharine causes a distraction allowing him to successfully steal the third scroll. Tintin gives chase, but Sakharine gains all the scrolls by ordering his gang to toss Captain Haddock and Snowy into the water, forcing Tintin to rescue them instead of saving the scrolls. Sakharine escapes, and Tintin is ready to give up but is persuaded by Haddock to continue. With help from officers Thomson and Thompson, Tintin and Haddock track Sakharine down, who is revealed to be a descendant of Red Rackham. They head back to their starting point and set up a trap, but Sakharine uses his pistol to resist arrest. His gang fails to save him, so Sakharine challenges Haddock to a final showdown. Sakharine and Haddock sword-duel with cranes and swords, but Sakharine is defeated and pushed overboard by Haddock. When climbing ashore, Sakharine is arrested by Thomson and Thompson. Tintin gathers the three scrolls and uncovers the solution to their riddle, leading him back to Marlinspike Hall. There, Tintin and Haddock find Red Rackham’s treasure and a clue to the Unicorn’s location in a walled-off room in the cellar. The film ends with both agreeing to continue their search for the shipwreck.