In 1955, 17-year-old journalist Tintin and his dog Snowy are browsing in an outdoor market in Brussels, Belgium. Tintin buys a miniature model of a ship, the Unicorn, but is accosted by an Interpol officer, Barnaby, and a dreaded ship collector, Ivan Ivanovitch Sakharine, who both unsuccessfully try to buy the model from Tintin. Tintin takes the ship home, but it is accidentally broken in an incident with Snowy and a cat in his apartment. A parchment scroll slips out, and rolls under the furniture, with Tintin not noticing it. Meanwhile, bumbling police detectives Thomson and Thompson are on the trail of a pickpocket, Aristides Silk.
After a visit to Maritime Library to search for clues, Tintin returns to find that the Unicorn has been stolen. He visits Sakharine in Marlinspike Hall and accuses him of the theft. When he sees a miniature model of the Unicorn, he notices that Sakharine’s model is not broken, realizing that there are two Unicorn models. Returning home once again, Snowy shows him the scroll . After reading an old message written on it, they are interrupted by the arrival of Barnaby, who is then assassinated while attempting to recover the Unicorn one last time. Tintin places the scroll in his wallet, but it is stolen by Silk the next morning, after a scuffle with the police detectives.
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 captain. Haddock is permanently drunk and thus unaware of the happenings on board his ship. Tintin, Haddock, and Snowy eventually outrun the crew, and escape from the Karaboudjan in a lifeboat. The ship fails to ram their boat, because they instead rammed an empty lifeboat the captain accidentally released during his escape. Presuming them to have survived by the number of lifeboats, Sakharine sends a seaplane to find and capture them. The trio seize the plane, and use it to fly towards the fictitious Moroccan port of Bagghar. However, the seaplane crashes in the desert due to low fuel.