Anatoly Schura graduated from the Belarusian State Conservatory. According to Alfred Schnittke's recommendation he was adopted by the Union of Soviet Composers in December 1990. In 1996-2001, Anatoly Schura was studying symphony conducting at the Estonian Academy of Music in the class of Professor Roman Matsov. He participated in master-classes of Jorma Panula. He has toured in Russia, Finland, Poland, Germany.

In 1991-92 Anatoly Schura was a director of the chamber orchestra of the Smolensk Philharmonia. In 1994, he created the Narva Symphony Orchestra.

Winner of Kultuurkapital Fund Prize for the popularization of classical music and the "Pearl of Culture" award. In February 2008, A.Schura was awarded the Order of the White Star V degree by the President of the Republic of Estonia.