In 1957, Klimov graduated from the Higher Institute of Aviation in Moscow. He considered a career in journalism before settling on cinema. He enrolled at the state film school, the Gerasimov Institute of Cinematography, where he studied under acclaimed director Efim Dzigan. While a student at the institute, Klimov met Larisa Shepitko, whom he would later marry. In 1983, he was a member of the jury at the 33rd Berlin International Film Festival.