Aleksandr Baluev was born in Moscow, Russian SFSR, Soviet Union. He graduated in 1975 from Moscow School № 637. After unsuccessful attempts to enter the Boris Shchukin Theatre Institute he worked for a year as assistant illuminator in the light department at Mosfilm. The second attempt was more successful, with Aleksandr entering the Moscow Art Theatre School on Pavel Massalsky's course. In 1980, he successfully completed the training and became an actor of the Soviet Army Theatre. The first role in his theatrical career was playing in productions of Clock Without Hands and Lady of the Camellias.
In the late 1980s, Aleksandr Baluev left the theater. He is now active in the entreprise, collaborates with the Lenkom Theatre.
In 1986, Aleksandr Baluev went to the Moscow Yermolova Theatre, playing leading roles in productions of The Second Year of Freedom, Snow Near the Prison, and Caligula.