After Shue Ming-Shu graduated from school he worked in an umbrella factory and a steelworks. In his spare time Shue would repair bicycles, in addition to putting in lots of hours of riding them. When he competed in races, he demonstrated skills across all distances and types of events, winning multiple gold medals. In 1959 he competed at the 14th Provincial Games before becoming a regular competitor for the Taiwan national team during the next decade. In 1964 he competed on both the road and track at the Tokyo Olympics, finishing 87th in the road race and 25th in the team time trial. Four years later Shue returned to the Olympics, finishing 29th in the team time trial at the Mexico City Games. After he retired he designed and promoted his own training programme in Taiwan.