This epic animation tale brings to life the adventures of Tintin, a journalist and his dog Snowy as they find themselves embroiled in a serious and suspenseful investigation. While they are browsing in an outdoor market in 1955 Brussels, Belgium. 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 finds that the Unicorn has been stolen. He then 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 and after reading a message written on it, Tintin puts the scroll in his wallet—but it is stolen by Silk.
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 but turned out to be the last surviving descendant of Sir Francis Haddock. 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 the lifeboat. This fails because they instead notice an empty lifeboat that the Captain accidentally released before the escape and ram it instead. Presuming them to have survived by the number of lifeboats; Sakharine sends a seaplane to find them, which the trio seize and use to fly towards the fictitious Moroccan port of Bagghar, but the seaplane crashes in the desert.
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 and after his eventual surrender, Sir Francis sank the Unicorn, and most of the treasure, to prevent it from falling into Rackham's possession.
It transpires that there were three Unicorn models, each containing a scroll; together, the scrolls can reveal the location of the sunken Unicorn and its treasure.
The third model is in Bagghar, possessed by Omar ben Salaad. Sakharine causes a distraction in a concert that results in him successfully stealing the third scroll. After a chase, he gains all the scrolls by having his gang toss Captain Haddock and Snowy in the ocean to force Tintin to go after him instead of saving the scrolls. After the boat leaves, Tintin is ready to give up but is persuaded by Haddock to continue.
With help from officers Thompson and Thomson, 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. When his gang fails to save him, Sakharine challenges Haddock to a final showdown. Sakharine and Haddock sword-duel with cranes and swords eventually resulting in Sakharine being defeated and pushed overboard the ship.
When climbing ashore, Sakharine is arrested by Thomson and Thompson. Guided by the three scrolls indicating the location of Marlinspike Hall, Tintin and Haddock find there some of the treasure and a clue to the Unicorn 's location. The film ends with both men agreeing to continue their search of the shipwreck.