Levenson was born in Johannesburg. He represented South Africa in the 1976 Eisenhower Trophy and turned professional in 1978 and spent his career mainly on the Southern Africa Tour and the European Tour. He won five titles in South Africa, including one South African Open Championship and one South African PGA Championship, and topped the Order of Merit in 1983/84. His two wins on the European Tour came at the 1979 Belgian Open and the 1991 Open de Baleares. Since turning fifty he has played on the European Seniors Tour, where he won the 2004 Barbados Open on his second outing.
European Seniors Tour