In recent years, the complexities of wind turbine control are raised while implementing grid codes in voltage sag conditions. In fact, wind turbines should stay connected to the grid and inject reactive power according to the new grid codes. Accordingly, this paper presents a new control algorithm based on super-twisting sliding mode for a gearless wind turbine by a permanent magnet synchronous generator (PMSG). The PMSG is connected to the grid via the back-to-back converter. In the proposed method, the machine side converter regulates the DC-link voltage. This strategy improves low-voltage ride through (LVRT) capability. In addition, the grid side inverter provides the maximum power point tracking (MPPT) control. It should be noted that the super-twisting sliding mode (STSM) control is implemented to effectively deal with nonlinear relationship between DC-link voltage and the input control signal. The main features of the designed controller are being chattering-free and its robustness against external disturbances such as grid fault conditions. Simulations are performed on the MATLAB/Simulink platform. This controller is compared with Proportional-Integral (PI) and the first-order sliding mode (FOSM) controllers to illustrate the DC-link voltage regulation capability in the normal and grid fault conditions. Then, to show the MPPT implementation of the proposed controller, wind speed is changed with time. The simulation results show designed STSM controller better performance and robustness under different conditions.