This vessel was a pirate ship of an unnamed pirate Captain.
During his mortal life, the captain lost his sword in battle and promised to get it back as his ship sunk. As a ghost, the captain raised his ship from the bottom of the sea and sailed to Port Royal to find his sword. The captain terrorized Port Royal until Will Turner forged a fake sword to replace the ghost captain's lost weapon. After that, the captain and his ghost ship disappeared.