The High-finned sperm whale is a supposed variant or relative of the known sperm whale that is said to live in the seas around the Shetland Islands in Europe. The major difference between this creature and other sperm whales is the presence of a tall dorsal fin on its back, which the known sperm whale, Physeter macrocephalus, lacks. Two such stranded whales were supposedly observed by Sir Robert Sibbald. He described their dorsal fins as being similar to a "mizzen mast".

Although species cannot be given scientific names until a type specimen is discovered, Physeter tursio has been suggested as the High-finned Sperm Whale's scientific name by an early observer.