Gustav Naan was born in Russian SFSR in a village near Vladivostok to a family of Estonian settlers. He graduated from the Leningrad State University in 1941. He took part in World War II and joined the CPSU in 1943. Having settled to Estonia after the USSR annexed Estonia, Gustav Naan, a loyal communist and graduate of the Higher Party School of the AUCP(b) (1946). published a number of Stalinist-oriented polemic pieces (treating Estonian history and politics from the pro-Soviet perspective, e.g. "Eesti kodanlike natsionalistide ideoloogia reaktsiooniline olemus″ ('The Reactionary Essence of the Ideology of Estonian Bourgeois Nationalists'), 1947). In 1948, Naan published an article in Voprosy filosofii on the philosophical implications of the theory of relativity, criticizing 'physical idealists' of the US and Britain; in 1951, however, he published an article that decried vulgar materialist critics of the relativity theory whilst being ″tolerant on philosophic questions to a striking degree in Stalinist Russia, considering its place and time of publication″. Authors who followed Naan's article into discussion were almost universally critical of Naan's position. In 1952, which was the most intense year of the debate, three different authors published against Naan in the 1952 first issue of Voprosy filosofii alone.
Naan was the director of the Institute of History of the Academy of Sciences of the Estonian SSR (1950–1951), Vice-President of the Academy of Sciences of the Estonian SSR (1951–1964). From 1964, Naan worked at the Institute of Astrophysics and Atmosphere Physics of the Academy of Sciences of the Estonian SSR. Having turned to theorizing on cosmology, cybernetics and demography, he often rejected taboos of both the 'traditional' world-view and orthodox communist opinions on such matters. He later claimed to have been one of the promoters of the theory of relativity at the time this was still considered pseudoscience by the Soviet authorities. He also proposed the Symmetric Universe hypothesis, according to which, side by side with the ordinary world, there is an anti-world.
Naan was editor-in-chief of Eesti nõukogude entsüklopeedia (literally: Estonian Soviet Encyclopedia), the first edition of which started in the late 1960s.
In terms of political affiliations, Naan remained a staunch supporter of the communist system and was a devote opponent of Estonia's pro-independence movement; Naan supported the (pro-Moscow) Internationalist Movement. Having gained much public support in the 1970s for his relatively bold opinion pieces on topics like family, morals and sex, he soon became a despised figure for his anti-independence stance, which was reflected in his newspaper articles of the time (e.g. his article «С ног на голову» ('From (standing on) Feet to (standing on) Head', Estonian title "Kõik pea peale″), condemning the Estonian Sovereignty Declaration passed by the Supreme Soviet of the Estonian SSR, was published in Pravda, 23. November 1988.).
Gustav Naan was despised by many who considered him a careerist and schemer.