Joan Marjorie Coxsedge (born 5 January 1931) is an Australian artist, activist, and a former politician. She was one of the first two women elected to the Victorian Legislative Council in 1979.
Joan Rochester was born in Ballarat, Victoria. Following school she worked as a professional artist. She joined the Australian Labor Party in 1967. She became involved with the Save Our Sons Movement, opposed to conscription for the Vietnam War, and in 1971 was imprisoned for anti-conscription activities. She was imprisoned with four others from the 'Save our Sons' organisation. In 1973 she was the founding chairman of the Committee for the Abolition of Political Police.
She unsuccessfully stood for election for the Victorian Legislative Assembly at the 1973 and 1976 elections. In 1979 she was elected to the Victorian Legislative Council and served until 1992.