A dynamic vibration absorber was proposed to improve the fluid induced vibration stability of a centrifugal compressor rotor system. First, the dynamic model of the rotor system under fluid excitation was established. Second, the Lyapunov theory was applied to study the fluid induced vibration stability of the rotor system with attached the dynamic vibration absorber. Then the influences of the absorber parameters on the stability of the rotor system were analyzed, which were verified by numerical simulations. The results show that the dynamic vibration absorber can effectively increase the instability speed of the rotor system, and the natural frequency and damping ratio of the absorber have influences on the stability of the rotor.