Benkow was born on 15 August 1924 in Trondheim, Norway. He was raised in Bærum, Norway. Benkow married twice, his second marriage was with fellow politician Annelise Høegh. He was the uncle of journalistic fraudster Bjørn Benkow. Benkow died on 18 May 2013 from natural causes in Oslo, Norway, aged 88.