Zeman was born on November 3, 1910, in Ostroměř (near Nová Paka) in what was then Austria-Hungary. In the 1920s, he studied at a French advertising school, and worked at an advertising studio in Marseilles until 1936. It was in France that he first worked with animation, filming an ad for soup. He then returned to his home country (by now Czechoslovakia), after visiting Egypt, Yugoslavia, and Greece.
Back in Czechoslovakia, Zeman advertised for Czech firms like Baťa and Tatra. At Baťa's window-dressing school, where he was teaching, Zeman met the animator Elmar Klos and showed him a sample of his work. Klos offered Zeman a job at Zlín's animation studio. After some consideration (his wife and children were already established in Brno), Zeman accepted the job in 1943. At the studio, Zeman met the pioneering animator Hermína Týrlová and, collaborating with his brother Bořivoj Zeman, made his first short film, Vánoční sen (1945).
Zeman then went on to solo work, including a series of shorts starring a puppet called Mr. Prokouk. His half-hour film Král Lávra (1950), from the poem by Karel Havlíček Borovský, won him a National Award, and was followed by his first feature film, Poklad ptačího ostrova (1952). His most unusual film may be the short Inspirace (1948), which tells a wordless, poetic love story using animated glass figurines.
It was in 1955, however, that Zeman began the work for which he is probably most famous: six feature films that combine live-action and animation techniques to create artistic visual styles. These were:
After this, Zeman experimented with more classical forms of animation, beginning with seven shorts about Sinbad the Sailor which were then expanded into the feature film Pohádky tisíce a jedné noci (1974). His final films were Čarodějův učeň (1977), from the novel The Satanic Mill by Otfried Preußler, and Pohádka o Honzíkovi a Mařence (1980).He died in Zlín on April 5, 1989, a few months before the Velvet Revolution.