Summary: An affine nonlinear model of three-phase shunt Active Power Filter (APF) is built by the state-space average modeling method and it is theoretically verified that the model satisfies the conditions of state feedback exact linearization. Based on the differential geometry, the nonlinear controller is designed to implement the decoupled control of APF. The proposed control scheme solves the nonlinearity problem of the model system completely in the whole operating range, and enhances the dynamic responses of the system. Simulation results based on the detection and control method are given showing that the proposed nonlinear control strategy is valid and feasible.