He played junior hockey with the Quebec Citadelles, Montreal NDG Monarchs, and the Montreal Junior Canadiens from 1961-66. Grenier turned pro with the Canadiens' farm team Houston Apollos in 1966-67. He earned callups with the Canadiens in 1968-69 and 1969-70. In 1970 he was traded to the Los Angeles Kings in part for Wayne Thomas and Leon Rochefort. He played two full seasons for the Kings but missed 1972-73 due to an ankle injury suffered in training camp. Two part seasons with the Omaha Knights and he retired in 1975.