He was born in 1963 in Taganrog into a family of musicians. He began studying the violin at the age of four under his father, the eminent pedagogue Mikhail Kuznetsov. In 1981, he began solo studies in the class of Professor B. Kotorovich at the Kyiv Conservatory. In 1986, he became a laureate of the H. Wieniawski International Violin Competition in Poland, and in 1987, a laureate of the N. Paganini International Violin Competition in Genoa, Italy.

Since 1991, the artist has lived and worked in Wrocław. In 2003/2004 he was the originator and organiser of the International N. Paganini Festival and the International Violin Competition "Young Virtuoso". He is the founder and artistic director of the Ricordanza Wrocław Soloist Ensemble and the Wrocław Festival Orchestra. He has recorded many albums with these ensembles, including one commissioned by the Wratislavia Cantans International Festival in 2002 (a reconstruction of N. Paganini's 1829 concert in Wrocław).

The J. Zeidler Musical Society commissioned him to create the album Musica Sacromontana, which won the prestigious "FRYDERYK" music award in 2008. The artist gives concerts both in Poland and abroad: in Germany, Norway, France, Spain, Belgium, Luxembourg and Switzerland. His "excellent and inspiring playing style has been appreciated by the most demanding audiences" ("Tagesspiegel").

Since his debut at the Berlin Philharmonic in 2004, the artist has regularly appeared as a soloist on this prestigious music stage. Viktor Kuznetsov has been teaching violin at the K. Lipiński Academy of Music in Wrocław since 1991. Since 2002, he has served as vice-president of the Wrocław Concert Society. Since 2013 he has been the president of the ESKM Foundation (European Youth Culture Network), whose main task is to promote young talented artists. He is the initiator and co-founder of the Wroclaw University Philharmonic in 2018, where he serves as artistic director.