HMS Grampus (S04) was a Porpoise-class submarine. Her keel was laid down in 1955 by Cammell Laird at Birkenhead. She was commissioned in 1958.
On 1 April 1963, Grampus returned to Gosport after spending three weeks under the polar icecap looking for holes in the ice. During the patrol she superficially damaged her hull on the ice.
On 11 January 1968, the French trawler Fomalhaut caught Grampus in her nets in the English Channel. Grampus surfaced and both crews spent over three hours disentangling the nets.
Grampus operated with USS Tigrone in a joint American-British oceanographic operation in the eastern Atlantic in 1972.