The purpose of this paper is to present a control strategy using Multiple Input/Multiple Output (MIMO) Second Order Sliding Modes (SOSM) for a grid-connected variable-speed Wind Energy Conversion System (WECS). The latter is based on a Double Fed Induction Generator (DFIG) in a bidirectional configuration with slip power recovery. Its points of operation can be electronically controlled and, with them, two independent control objectives can be stated. Thus, a control is designed to maximize the energy captured from the wind and to regulate the stator reactive power, contributing to the compensation of the power factor according to grid requirements. The proposed technique can be applied to nonlinear MIMO systems and allows to make a separate design for each component of the controller. For these designs the Super-Twisting algorithm is employed in this work, which possesses excellent properties regarding simplicity of implementation and online operation, and robustness against uncertainties and external disturbances. Finally, representative simulation results are presented and analyzed. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.