In order to reduce the vibration response of the air turbo rocket （ATR） engine， a finite element model is established for the rotor structure characteristics of the engine. The squeeze film damper is designed. And the dynamic characteristics are analyzed and tested. The results show that the main strain energy of first-order mode of the ATR rotor is concentrated in the first bearing， and the main strain energy of second-order mode is concentrated in the second bearing. After the squeeze film damper is designed at the first bearing， the rotor can obviously reduce the first-order response， but the damping degree of the second-order response is limited. The application of the squeeze film damper on the ATR rotor has a significant effect on reducing the vibration response of the rotor， and make the rotor of ATR engines increase steadily to the working speed.