He started to play the cello at the age of five. In 1995 he completed his studies at the Musik Academy of Moscow and then continued his postgraduate studies in the master class of David Geringas in Lübeck (Germany).
In 1997, Alexander Neustroev was named best Russian cellist at the Rostropowitsch Contest in Paris. In 1998, he was award winner at the Tschaikovsky Contest in Moscow. In 2001, he won the first prize at the International Australasian Adam Cello Festival & Competition in Christchurch (New Zealand), and, at the same contest, the special prize for best interpretation of Astor Piazzolla\'s Le Grand Tango.
In March 2002, he performed as soloist with the Zürich Tonhalle Orchestra under the direction of Lorin Maazel. This concert was broadcast by Swiss Radio DRS 2. In 2003, Alexander Neustroev was soloist on a concert tour with the New Zealand Symphony Orchestra.
He has made a lot of CD records for television and radio (among others - Double Concerto J. Brahms played with Bartek Niziol). He regularly gives lectures during master classes in Switzerland, Germany and Russia. Since 1999, Alexander Neustroev has been assistant principal cellist in the Zürich Tonhalle Orchestra.