Olsen was twice the parliamentary leader of the South Australian Division of the Liberal Party of Australia in the South Australian House of Assembly, from 1982 to 1990 and again from 1996 to 2001. He unsuccessfully led the party to both the 1985 election and 1989 election. After the 1989 election he left South Australian parliament to fill a casual vacancy in the Australian Senate. He returned to the South Australian parliament in 1992, but was defeated for the Liberal party leadership by Dean Brown.