Alexander Anisimov was born in Moscow, started his musical education at the Moscow Choir School named after A. V. Sveshnikov and the Leningrad Choir School named after M.I. Glinka. Studied at the Leningrad State Conservatory. Named after N. A. Rimsky-Korsakov (class of choral conducting of E. P. Kudryavtseva), the Moscow State Conservatory named after P. I. Tchaikovsky (class of opera and symphonic conducting by O. A. Dimitriadi and L. M. Ginzburg) and Graduate School (class of G. N. Rozhdestvensky).

The professional career of the musician has begun at the Leningrad Small Opera and Ballet Theatre named after M.P. Mussorgsky (now Mikhailovsky). In the 1980s he worked with leading musical theatres and orchestras of the USSR. Since 1985, he began to cooperate with the Leningrad Opera and Ballet Theatre named after S. M. Kirov (now the Mariinsky), where he conducted the prime compositions of the opera and ballet repertoire, as well as symphonic programs. In 1993 he worked with Mstislav Rostropovich on B. Britten’s War Requiem in Great Britain and Spain.

In 1980-1984 and 1989-2003 — took a position of a Chief Conductor of the Bolshoi Theatre of Belarus. In 1985–1989 — Chief Conductor of the Perm Opera and Ballet Theatre (staged the first production of the opera Fiery Angel by S. Prokofiev in the USSR (1984), in 1998–2001 — National Symphony Orchestra of Ireland (RTÉ), 2005–2009 — Busan Philharmonic Orchestra (Republic of Korea), 2003-2007 — Rostov State Musical Theatre. In 2011-2017 — Artistic Director and Chief Conductor of the Samara Academic Opera and Ballet Theater. For the Rostov production of Lady Macbeth of the Mtsensk District Alexander Anisimov was awarded the Golden Mask in the nomination “Opera/ Conductor” (2005).

Since 2002 he has been an Artistic Director and Chief Conductor of the State Academic Symphony Orchestra of the Republic of Belarus; in 2018  maestro returns to the National Academic Bolshoi Opera and Ballet Theatre of the Republic of Belarus as a guest conductor.

During the years of his work at the Belarusian State Philharmonic Society and the The National Academic Opera and Ballet Theater of Republic of Belarus, Alexander Anisimov presented the best examples of classical heritage and premieres of new works to the public in Belarus and abroad, among them: symphonies of L. van Beethoven, P. Tchaikovsky, S. Rachmaninoff, S. Prokofiev, D. Shostakovich; orchestral works of R. Strauss, R. Wagner, G. Мaler, G. Gershwin, М. Ravel; first musical performances of D. Smolsky, А. Mdivani, М. Kuznetsov, G. Gorelova; premieres of operas and ballets by М. Glinka Ivan Susanin, P. Tchaikovsky The Nutcracker, Iolanta, А. Borodin Prince Igor, G. Bizet Carmen, Y.Semenyako A New Land, Е. Glebov Kurgan, The Master and Margarita, V. Soltan King Stakh’s Wild Hunt, S. Prokofiev Мaddalena.

Under his leadership of the student’s Symphony orchestra of the Belarusian state Academy of music has prepared programs for performances on the stages of the Belarusian State Philharmonic Society, the Moscow Conservatory and Germany.