Hans-Georg Beyer came from a top sporting family. His brother Peter and his sister Angelika also played handball, his brother Udo won Olympic gold in 1976 and bronze in 1980 as a shot putter, his sister Gisela finished fourth in the 1980 Olympic discus, while another sister, Gudrun, became physiotherapist to the German fencing team in 1992.
Hans-Georg Beyer won the 1975 and 1982 East German titles with ASK Vorwärts Frankfurt, and won the 1975 European Cup. He scored the decisive goal in the final against the USSR in the 1980 Olympic final and won an Olympic gold medal. Beyer earned 46 caps for East Germany and retired in 1982 after spinal surgery. He then turned to coaching.