When the load is reduced to a certain degree，the compressor will produce dramatic instabilities. The instabilities are inherent of axial compression system，including rotating stall and surge.Although the traditional control method can guarantee the security of the compressor，but it narrows the operating range of compressor and seriously influences compressor performance.In order to improve the active control effect on instabilities，first，for the reason of simple structure and conspicuous effect，the close-coupled valve(CCV)was selected as an active actuator to be used in the compressor system in this paper.At the same time the dynamic mathematics model with CCV was built based on the classical MG model and unstationary theory.Then the active control law under conditions of constant speed and non-constant speed was designed based on the backstepping method and was applied to the simulation of the rotating stall and surge with the active control law in different times，then the influence brought by parameter B was evaluated.Finally，the results of the simulation validated the effectiveness of the active control law and proved the high effect of the CCV actuator on the control.