This paper proposes a super-twisting second order sliding mode control scheme to maximize the wind energy capture of a doubly fed induction generator based variable speed wind turbine (VSWT) system, and minimize the reactive power simultaneously. Two second order sliding mode controllers are designed to achieve the control objectives, reduce mechanical stress and improve control accuracy. By regulating the generator rotor voltage, one controller makes the wind turbine rotor speed track the optimal speed, which can maximize power generation. The other maintains the rotor current at rated value to minimize the reactive power. A quadratic form Lyapunov function is adopted to determine the range of controller parameters and guarantee the finite time stability. Simulation results on a 1.5 MW doubly fed induction generator (DFIG)-based variable speed wind turbine demonstrate the validity of the proposed control strategy.