In order to improve the dynamic performance of double-fed wind generator (DFIG) grid-side converter (GSC), a nonlinear compound control strategy is proposed based on GSC affine nonlinear model. In this control, the feedback linearization decoupling of the current is performed under stationary coordinate system and no need of grid voltage orientation instead of conventional feedback linearization. Simultaneously, sliding mode control based on a saturation function is applied to the voltage loop, which achieves fast stabilization of the DC-bus voltage and the current tracking. The stability of the GSC and the control of power factor on the grid side are achieved through simulation, which verify the correctness of the theory. Compared with the traditional control method, the control strategy proposed in the paper can reduce the variables of calculation and ensure the rapid convergence of the system.