This study proposes a power control strategy for a grid-connected variable-speed wind turbine, based on a doubly-fed induction generator (DFIG) with slip power recovery. The control objectives vary with the zones of operation (dependant on the wind speed), aiming to maximize the active power in the partial load zone and to limit it when operating within the full load zone, while regulating the stator reactive power following grid requirements. The control design, based on the second-order sliding modes (SOSM) and Lyapunov, uses a modified version of the super-twisting algorithm with variable gains which can be applied to nonlinear multiple inputs-multiple outputs (MIMO) systems. The well-known robustness of the sliding techniques, the simplicity of the algorithm, and the adaptive characteristic of its gains are used together in this study to obtain a controller able to deal robustly with the exacting challenges presented by these systems. An additional benefit of the proposal lies in the smoothness of the control action, an important issue regarding applied mechanical efforts. Representative results obtained by simulation of the controlled system are shown and discussed.