He was born in Saint-Petersburg. After graduating in 1990 Musical school named after M.P. Musorgsky (class of conducting by L. Grigoryev) he entered in Saint-Petersburg academy of culture on the department of orchestra conducting (class by prof. I. Musin) where he took an external degree.

During 1993 – 1998 years he was studying in Saint-Petersburg conservatory named after N.A. Rimsky-Corsakov on the faculty of opera-symphonic conducting (class by prof. I. Musin).
Since 1991 he has became artistic leader and conductor of Youth chamber orchestra of Saint-Petersburg state university. In 1993 for the work with this orchestra he was rewarded with grant of President of Russia and Ministry of Culture.

Since 2004 he has worked in the capacity of Chief conductor of Saint-Petersburg theatre of musical comedy. He has been the musical leader of following performances: «Bluebeard» and «Orpheus in the Underworld» by J. Offenbach, «The Merry Widow» and «The Count of Luxembourg»W by F. Lehar, «Baroness Lili» by J. Huszka, «Gasparone» by K. Millocker, «Bayader», «The Duchess from Chicago» and «The Violet of Montmartre» by I. Kalman, «The Bondmaid» by N. Strelnikov, «The Bird Seller» by C. Zeller, «The Secret Garden» and «Tom Sawyer» by S. Banevich, «Womanish revolt» by E. Ptichkin, «Shoo!» by Y. Dubravin, «Grooms» by I.Dunaevsky, «Hollywood diva», «Bely. Petersburg» by G. Firtich, «Cabaret for gourmets», «Wedding in Malinovka» by B. Alexandrov, «Cox&Box in a court» by A. Sullivan, «Cin Ci La» by C. Lombardo and V. Ranzato.

As an invited conductor he performed with many symphonic, opera and chamber orchestras of the country.

In 2007 A.V. Alekseev was given the rank of «Honored artist of Russia».

In 2016, among the creative team of performance «Bely.Petersburg» was awarded the Prize of the Government of St. Petersburg in the field of culture and art for 2015 «for achievements in the field of music and performing arts».

In 2017 he was given the Highest national theatre prize of Russia «Golden Mask» in the nomination «Best conductor» in the play «Bely. Petersburg».