Klein studied law in Heidelberg and Munich, where he graduated with his Ph.D. in 1961. Then he moved to the Management Service of Baden-Wuerttemberg, lost but not the scientific career from his eyes, which led 1967 Habilitation on the topic "Participation of the state in economic competition with Ernst Forsthoff at the University of Heidelberg. In 1969 Hans Hugo Klein became a professor for Public Law at the University of Göttingen. In 1970, he joined the CDU, where he was the German Bundestag from 1972 to 1983. He moved in 1972, 1976 and 1980, one of the Land of Lower Saxony CDU in parliament, winning 1983, the direct mandate in the constituency of Göttingen.[2]
In 1983 he was appointed as a judge of the Constitutional Court. During his tenure at the Federal Klein belonged to the Second Senate of the court. His responsibilities with the Federal Party were right, the right of the public service and staff representation rights.[2] He was succeeded by Hans-Joachim Jentsch.