Anatoly Zverev was born on November 3, 1931, in Moscow.

He was the seventh child in a large family of the Civil War veteran Timofey Zverev, working as an accountant in the peacetime, and Pelageya Zvereva – an unskilled worker. Of nine children of the family, only three - Tolya and sisters Zina and Tonya - survived.

His father died in his early childhood. Anatoly Zverev lived with mother first in Sokolniki, then in the Sviblovo area. Pelageya Zvereva died in 1979.

Since his early childhood, Zverev had been lonely and flotsam; his development and education were mostly self-development and self-education.

He visited the art studios in Sokolniki and Izmailovo, where the artists who preserved the ideals of modernist and early avant-garde art (Sergey Sokolov, Vladimir Rozhkov) taught art. At the art school, Zverev was mentored by Nikolay Sinitsyn, a student of Ostroumova-Lebedeva.

Later Zverev was trained in a tradesmen school as a painter-decorator.

Having acquired the trade of painter, Zverev got a job in the Sokolniki park. There, the artist who painted children's playgrounds was noticed by Alexander Rumnev. He was the first discoverer of the Zverev's talent and his patron for many years..

In 1954, Zverev met the famous art collector George Costakis. Costakis was one of the most significant figures in Zverev's biography - he made out an ingenious graphic artist and a painter in the young artist.

In 1957, in the course of the Festival of Youth and Students in Moscow, the Mexican artist Siqueiros awarded Zverev with the highest prize. That's how it was. A "competition" of artists took place in the Gorky Park. A young man from America Gary Colemen arranged live performances there, spraying paints on a canvas like Jackson Pollock. Zverev accepted the challenge - he spread a vast canvas and painted an expressional portrait. The judge of an artistic competition - the Mexican modernist David Alfaro Siqueiros - awarded (informally) Anatoly Zverev with the first prize. Also he gave his palette knife as a present. Even if the participation and the victory of Zverev in the Festival is a legend, then its creation was not accidental. The artist was associated with all new and fresh in the art. Igor Markevich wrote later about that time: "… There were new people surprisingly free from all prejudices".

In 1957 Anatoly Zverev married Lyudmila Nazarova. They had two children: a son Mischa and a daughter Verochka. But the family life did not last for long - soon they divorced, and Zverev saw very little of his children.

In the mid-1960s, Zverev met Vladimir Nemukhin, then Dmitry Plavinsky – George Costakis invited him to Lianozovo where the non-conformist artists gathered around Evgeny Kropivnitsky and Oscar Rabin.

Zverev felt a creative bond with these unrecognized and, in his words, "modern" artists. Many of them remained his friends for the rest of his life. However, Zverev himself did not participate in any considerable performances and events associated with the underground art (the exhibition of the Moscow Regional Union of Artists in the Manege, the "Bulldozer Exhibition", etc.). He was on his own in life and art.

In 1960, the Life Magazine came out with the Zverev's reproductions and the article of Alexander Marshak named "The Art of Russia that Nobody Has Seen". It was vivid evidence of the global recognition of the artist. At the same time in Russia, Zverev remained an underground figure.

Zverev had no official workplace, did not join any unions and did not receive any state orders. He lived for his art, literally and figuratively. At the time when every person was built into a system, this step required a lot of courage. Zverev had to hide from the police ready to arrest him at any time "for social parasitism".

In 1965, the French-Swiss conductor Igor Markevich arranged a large exhibition of Zverev in the Parisian gallery of Motte, having accompanied it with his essay. There was a legend that Markevich had Zverev locked in his room at the Metropol Hotel for several days for him to paint a few new canvases for the exhibition. Anyway, in the mid-1960s, the name of the artist and his works became known in the West. The works were purchased by the large museums (first of all the MOMA in New York), they participated in the exhibitions of "the new Russian art". Zverev had never been abroad and had never attended any of the vernissages.

Zverev had a lot of infatuations, but only one love. In 1968, Anatoly Zverev got acquainted with Oksana Aseeva. In her early years, she was acquainted with Mayakovsky, Khlebnikov and Pasternak. In 1916, Oksana married the poet Nikolay Aseev, and in 1963 she became a widow. A meeting of Zverev and Aseeva had changed the life of them both. For many years, Oksana Aseeva remained a muse of Zverev. Aseeva died in 1985. The artist died one year later.

The paintings of Zverev were exhibited at home exhibition and collective displays of the non-conformists several times (the most well-known – in 1975 in the Beekeeping pavilion of the All-Union Exhibition of the Achievements of National Economy VDNKH).

However, the first and the only "personal exhibition" - the exhibition taking place in the Zverev's lifetime – was held not long before his deaths in 1984, in the City Committee of Graphical Artists in the Malaya Gruzinskaya Street. Vladimir Nemukhin was one of the main organizers.

Anatoly Zverev died on December 9, 1986.

According to eyewitnesses, the burial service held in the Temple of Elijah Obydenny (in the Obydensky Lane) gathered the people so prominent and refined, that the significance of a loss for the entire Moscow was absolutely evident.

The grave of the artist is located at the Dolgoprudny cemetery near the Novodachnaya platform. The author of the mortuary monument - an oak cross with the inscription "King of Glory" - Dmitry Plavinsky. Every year on December 9, close friends of Zverev meet there to honour his memory.