Grampus was built at the Washington Navy Yard under the supervision of naval constructor William Doughty, based on a design by Henry Eckford.

Lieutenant Francis Gregory commanded Grampus on her first cruise as part of the West Indies Squadron, which took her to the Antilles in pursuit of pirates.

In the company of Hornet, Enterprise, Spark, Porpoise, and Shark, Grampus engaged in convoying merchant vessels throughout 1821, the presence of the squadron having a marked effect on piratical activity among the islands.

The brig struck her colors and Lt. Gregory discovered that she was Palmyra, a Puerto Rico-based pirate carrying the papers of a privateer as a subterfuge.

Author Herman Melville created a fictional whaling ship in his novel Moby-Dick by the name of "Grampus", its crew briefly mentioned in Chapter 3 as they enter the Spouter Inn after a three years voyage.