Sudden imbalance, such as the disfigurement and the loss of blade for the high speed rotation machinery (e.g. aero engine) can lead to the instability and damage of the rotor. In this paper, numerical simulation is employed to study the sudden imbalance rubbing response of a rotor system. Results show that sudden imbalance leads to 6 different forms of rubbing response. The transitions of the steady?state response in the plane of parameter?rotation speed are given. The instability during the speed reduction after sudden imbalance is considered, and the stability boundaries of rotation velocity are also given. It is found that increasing the rotor damping as well as decreasing the contact stiffness and friction coefficient can reduce the unstable range of rotation velocity. Moreover, the influence of the parameters on transient responses of the system is investigated. It is shown that transient responses jump with the change of rotation speed. When the rotation speed is below the resonance speed, transient amplitude gently increases with the sudden imbalance eccentricity, but when it is above the resonance speed corresponding to a given eccentricity, the transient amplitude also jumps.