In this paper, a wind energy conversion system, which consists of a variable speed wind turbine with doubly-fed induction generator (DFIG) fed by a matrix converter is considered. The stator of the wind turbine driven generator is directly connected to the grid, while the rotor is connected via slip-rings to the output of a matrix converter. The matrix converter is supplied from the grid and replaces the conventional two back-to-back converters used for the control of a DFIG. Modeling of the energy conversion system considers super-synchronous and sub-synchronous operating conditions, which are achieved by means of the matrix converter. In order to decouple the active and reactive power, stator field oriented control is applied. Speed mode control is adopted for maximum wind energy extraction, provided that the wind speed and pitch angle of the turbine are known for each sampling period. Consequently, a 2-D lookup table calculating the reference speed by means of interpolation/extrapolation is introduced. Reactive power control is performed so that the stator reactive power is kept to zero. Promising simulation results demonstrating the control performance of the wind energy conversion system are presented.