In order to improve the low voltage ride through (LVRT) capability of doubly-fed induction generator (DFIG), a tracking control method for grid side converter (GSC) based on state-dependent Riccati equation (SDRE) technique is proposed. The grid code requires that wind farms should inject reactive power to support voltage recovery during LVRT process. In order to improve the supporting capacity of the nonlinear state-regulator on reactive power, nonlinear reactive power tracking controller is designed in GSC of DFIG, and the state feedback control law is obtained through solving state dependent Riccati equation. On the basis of maintaining the stability of DC link voltage in LVRT process, the reactive power regulation capability of GSC is fully utilized to provide reactive power support for the power grid to avoid voltage deterioration. Finally, a 9 MW DFIG-based wind farm is built by Matlab/Simulink. The simulation results show that the proposed GSC control method has good transient performance and effectively improves the LVRT capability of DFIG through simulation verification under three phase ground faults.