A current tracking control strategy for active power filters(APF) is proposed based on the switched system theory. Firstly, the switched affine dynamic model of APF is established. The quadratic stability of the system is proven based on the stability theory of the switched affine system and the voltage space vector method. A switching sequence is proposed consequently. In order to complete the digital realization of the controller, the discrete switched affine system model of APF is presented. An optimized switching rule is proposed to guarantee the optimal performance during each sampling period. Simulation results show that the proposed method can realize the accurate tracking of the reference current, decrease the switching frequency and improve the dynamic performance effectively.