A plane, carrying Tintin, a young journalist from Brussels, Captain Haddock, a sea captain and Tintin’s dog Snowy, is hit by lightning and crash lands in a desert, knocking Tintin, Snowy and Haddock unconscious.
The game then shifts to the previous day, where Tintin and Snowy are looking around a market. Tintin purchases a model ship, which another man tries to purchase from him, but fails. The man who sold it to him brings him to a friend of his who is a ship expert, who tells Tintin that the ship is called the Unicorn, a triple mast shiped, double-decked ship with fifty guns, which belonged to Sir Francis Haddock. The ship expert gives Tintin a book, and Tintin learns that the ship (which was a part of Charles II’s fleet) was on its way from Barbados to Europe when it was attacked by Red Rackham. Rather than be boarded, Sir Francis scuttled the ship and fled. Tintin then takes it to a back alley to examine it, finding a scroll hidden in it, which contains a strange poem about three ships. Suddenly, he is attacked by some men, who steal the ship. Tintin gives the scroll to Snowy, who sniffs one of the men’s hats, and leads Tintin to Marlinspike Hall. There, he meets the man who had attempted to get the boat in the market, one of the Bird brothers. The brothers chase after Tintin, attempting to get the scroll, but they are knocked unconscious by a man named Allan and his men. Allan then knocks Tintin unconscious as well.
Tintin wakes up on a ship called the Karaboudjan, but is freed by Snowy. Realising that Allan has stolen the scroll, Tintin goes to find him. However, he inadvertently climbs into the cabin of the original captain of the ship, who gives Tintin directions on how to find Allan. Tintin confronts Allan, who reveals that the former captain is a Haddock, and an ancestor of Sir Francis. Tintin manages to get the scroll from Allan and brings it to Captain Haddock, who agrees to tell Tintin the story of his ancestor.
The Unicorn was an enormous galleon that transported goods from various places to Europe. On the trip when it was attacked by Red Rackham, it was carrying gold, coins, diamonds and other precious treasures. Rackham and his men had attacked the Unicorn hoping to steal the treasure. As Haddock re-enacts the sword fighting of his ancestor, he destroys some electric cables, setting fire to the cabin, which ultimately causes the ship to sink. Tintin, Snowy and Haddock manage to escape and climb onto a seaplane. The rest of the crew also survives, and they too board the plane and escape.