Zaitsev was born in Yeleninskoye, Orenburg Governorate in a peasant family of Russian ethnicity and grew up in the Ural Mountains, where he learned marksmanship by hunting deer and wolves with his grandfather and older brother. He brought home his first trophy at the age of 12: a wolf that he shot with a single shot from his first personal gun (given to him by his Grandfather), a single-shot 20 gauge shotgun, which at the time he was barely able to carry on his back.