At the 1984 New York/Stoke Mandeville Paralympics, Hammond won three gold medals in the Men's 100 m Breaststroke A8, Men's 100 m Freestyle A8, and Men's 4x100 m Medley Relay A1–A9 events, and three silver medals in the Men's 100 m Butterfly A8, Men's 200 m Individual Medley A8, and Men's 4x100 m Freestyle Relay A1–A9 events.
At the 1988 Seoul Paralympics, he won two gold medals in the Men's 100 m Breaststroke A8 and Men's 100 m Freestyle A8 events, and a silver medal in the Men's 4x50 m Freestyle Relay A1–A8 event.
 During his swimming career, he was coached by Peter Ryan and Harry Gallagher.

He gave up swimming after the 1988 Summer Paralympics because he had achieved all his goals in that sport, and concentrated on sailing.
He was part of a Sonar team that was aiming to participate in the 1996 Atlanta Paralympics, but it did not qualify because it came ninth in a pre-games regatta in Florida.
His crew then prepared to sail at the 2000 Sydney Paralympics, but in November 1999, one of the members quit due to business reasons.
An old friend then invited him to participate in the volleyball campaign, and he became part of the men's "standing" team, where his height of 1.96 metres (6 ft 5 in) gave him a distinct advantage.
At the 1984 New York/Stoke Mandeville Paralympics, Hammond won three gold medals in the Men's 100 m Breaststroke A8, Men's 100 m Freestyle A8, and Men's 4x100 m Medley Relay A1–A9 events, and three silver medals in the Men's 100 m Butterfly A8, Men's 200 m Individual Medley A8, and Men's 4x100 m Freestyle Relay A1–A9 events. At the 1988 Seoul Paralympics, he won two gold medals in the Men's 100 m Breaststroke A8 and Men's 100 m Freestyle A8 events, and a silver medal in the Men's 4x50 m Freestyle Relay A1–A8 event.  During his swimming career, he was coached by Peter Ryan and Harry Gallagher.
He gave up swimming after the 1988 Summer Paralympics because he had achieved all his goals in that sport, and concentrated on sailing. He was part of a Sonar team that was aiming to participate in the 1996 Atlanta Paralympics, but it did not qualify because it came ninth in a pre-games regatta in Florida. His crew then prepared to sail at the 2000 Sydney Paralympics, but in November 1999, one of the members quit due to business reasons. An old friend then invited him to participate in the volleyball campaign, and he became part of the men's "standing" team, where his height of 1.96 metres (6 ft 5 in) gave him a distinct advantage.
Greg Hammond