Josip Pokupec was a representative of the Sokol cycling club in Zagreb when he was selected to compete for Yugoslavia at the 1936 Berlin Olympics. At the Games Pokupec competed in the road race at the Berlin Olympics where he finished the course, but his time was not recorded. In 1938 he became the Yugoslav national road race champion. One year later he came third in the same race in addition to winning a stage of the Tour of Serbia. After the war Pokupec emigrated to Canada and lived in Hamilton, Ontario.