Füsun Onur was born in 1938 in Istanbul. In 1960, she graduated under the supervision of Ali Hadi Bara from the Istanbul Academy of Fine Arts (now Mimar Sinan University) Sculpture Department. She received a Fulbright scholarship to study at the American University in Washington D.C., after which she spent four years at the Maryland Institute College of Art in Baltimore.

In 1970, Füsun Onur staged her first solo exhibition at Taksim Art Gallery in Istanbul. Since then she has staged many other solo exhibitions and has participated in biennials in Istanbul, France and Russia. She has also contributed to numerous group exhibitions, presenting her sculptures and installations in such countries as Belgium, the Netherlands, Great Britain, Macedonia, Germany, Austria, Sweden and New Zealand. Her recent exhibitions include Tactics of Invisibility at Pi Artworks (Istanbul 2010) and Tanas (Berlin 2010), and Silent Storm at the Port Izmir Festival (2010). In 2007, Yapi Kredi published a book of Füsun Onur's work, For Careful Eyes, written by Margrit Brehm for René Block's series Contemporary Art in Turkey. Füsun Onur lives and works in her family house on the Bosporus shore in Kuzguncuk.