Born in Otahuhu, Auckland in 1942, Max Grace began competing in the New Zealand national junior cycling race in the early 1960s. One year later Grace finished third in the senior event, followed by seventh in 1963. These performances earned him a place on the Olympic team for the 1964 Games in Tokyo where he placed 66th in the individual road race, only 0.2 seconds behind the race winner. By the end of the decade Grace moved to Canada, becoming a Canadian citizen, and won three consecutive national road race titles from 1970 to 1972. In 1970 he represented Canada in the road race at the British Commonwealth Games in Edinburgh, and again at the 1974 British Commonwealth Games in Christchurch. Grace was consistent in the Gastown Grand Prix criterium race in Vancouver, finishing second in 1973, first a year later, and third in 1975.