Klyuyev or Klyuev (Russian: Клюев) is a Russian surname. Notable people with the surname include:
Aleksandr Klyuyev, Russian football player
Andriy Klyuyev, Ukrainian businessman and politician
Andrey Kluyev, Russian cyclist
Artyom Klyuyev, Russian football player
Boris Klyuyev, Russian actor
Denis Andreyevich Klyuyev, Russian football player
Denis Klyuyev, Russian football player
Nikolai Klyuev, Russian poet
Serhiy Klyuyev, Ukrainian businessman and politician
Yury Klyuyev, Russian speed skater