Ivan Klyun was born Ivan Vasilyevich Klyunkov on 1873 in Bolshie Gorki village (near Moscow).
Ivan Klyun has studied at the Art School in Penza.
In 1889-1890 he studied at the school of the Society of the Encouragement of the Arts in Warsaw.
From 1890 to 1905 he studied art at the studios of F. Rerberg, Il. Mashkov and V. Fisher in Moscow.
From 1910 to 1914 he has participated in exhibitions of the group of artists Soyuz Molodyozhi (Union of Youth) together with David Burliuk, Wladimir Burliuk, Kazimir Malevich, Pavel Filonov, Vladimir Tatlin, Yuri Annenkov and others.
In 1915 Klyun participated in exhibitions of the group Tramway V. In the same year he joined the group of artists Supremus that was led by Malevich.
From 1917 to 1921 Klyun was Head of the Central Exhibition Bureau of the Fine Arts Department of Narkompros.
Ivan Klyun died in 1943, Moscow.