Behrendt was trained as a merchant and accountant. He took part in World War II and afterwards worked as clerk in an industrial firm. In 1954 he became a contributor to the company journal of Hoesch-Westfalenhütte AG in Dortmund. Behrendt joined SPD in 1932 being a member of the Socialist Working Youth (Sozialistische Arbeiterjugend). From 1945-1947 he was chairman of the regional Socialist Youth for Dortmund, Lünen and Castrop-Rauxel. He was chairman of the SPD branch in Dortmund-Altenderne in 1951/52 and in Dortmund from 1952 to 1955.
From 1952 until his death Behrendt was municipal councillor in Dortmund. In 1957 he was elected member of the Bundestag (electoral constituency: Dortmund III) and remained in office until 1976. Between 1961 and 1967 he was assistant chairman of the Labour Committee. Additionally, Behrendt was member of the European Parliament from 1967 to 1977 where he served as vice-president (1969–71, 1973–77) and president (1971–73). He was one of the signers of the Humanist Manifesto in 1973.
Behrendt was also member of the supervisory board of Dortmunder Stadtwerke AG and Dortmunder Hafen und Eisenbahn AG.