Valeri Klimov (born October 16, 1931) is a Russian violinist.
Klimov was born in Kiev (then in the Soviet Union, now in Ukraine). He was trained at the Odessa and Moscow Conservatories. While a disciple of David Oistrakh there, he was appointed a soloist at the Moscow Philharmonic Orchestra and won the inaugural violin edition of the International Tchaikovsky Competition.
Later in his life he was allowed to perform in the West, debuting at the Royal Festival Hall in 1967; he has performed abroad since. He was a People's Artist of the USSR.
He is now a teacher at the Moscow Conservatory.