Suleimenov was born on 18 May 1936 in Alma-Ata. He graduated from Geological Sciences Department of Kazakh State University in 1959. Suleimenov also finished Gorkii Institute of Literature in 1961. Between 1962-1971, he worked at Kazakhskaya Pravda. Suleimenov was awarded Komsomol Prize for Kazakhstan in 1966. Between 1969 and 1989 he was a member of the Communist Party of the Soviet Union. In 1981 he was a member of the jury at the 12th Moscow International Film Festival. He became First Secretary of the Committee of the Kazakhstan's Writers Union in 1983. He is a Russophone writer.
His most influential work AZ-i-IA was published in 1975. AZ-i-IA drew wide-scale criticism from the literary elite in Russia. Suleimenov was charged with "national chauvinism" and "glorifying feudal nomadic culture. Kazakhstan Communist Party first secretary Dinmuhammad Konayev intervened on Suleimenov's behalf; discussing the content of the book with Leonid Brezhnev and saving Suleimenov's career.
His other works include
Zemlia Poklonis' Cheloveku (1961)
Solnechnye Nochi (1962)
Dobroe Vremia Voskhoda (1964)
God Obez'iany (1967)
Glinianaia Kniga (1969)
Tiurki v Doistorii : o proiskhzhdenii drevnetiurkskikh iazykov i pis'mennostei (2002)
Suleimenov again became a worldwide name in 1989, when he led the establishment of the international environmental movement Nevada-Semipalatinsk. Nevada Semipalatinsk campaigned to close nuclear sites in Nevada and in the Semipalatinsk Province of Kazakhstan.
After independence, Suleimenov established the Peoples' Congress Party in 1991 and served as the speaker of Parliament until 1994. While at the Parliament, he rose to the position of opposition leader, engaging in several political struggles with President Nursultan Nazarbayev. Many opposition leaders urged him to run as a candidate in the next presidential elections.
In 1995, to preempt his potential candidacy, Nazarbayev brokered a deal, and Suleimenov was appointed as Kazakhstan's ambassador to Rome. From 2002 till now he serves as Kazakhstani ambassador at the UNESCO in Paris.