He then led Australia on a tour of the West Indies, then the strongest team in the world. He made only one half century, 67 in the Third Test in Georgetown, Guyana. It was the only Test that Australia won in a 3–1 series loss. He had a disappointing series scoring 199 runs at 22.11 and taking seven wickets at 52.28. Simpson wanted to continue playing Tests as Australia hosted Mike Brearley's Englishmen in 1978–79. His players wanted him to continue, but the Australian Cricket Board voted him out and installed Graham Yallop as the skipper. During his comeback, he had accumulated his 60th first-class century against Barbados during the Caribbean tour and become the oldest Australian to score a Test century on home soil.