This paper presents a new variable speed wind energy conversion systems (WECS). It is based on a six-phase asymmetrical squirrel cage induction generator (SCIG) and a matrix converter (MC) as power electronic interface between six-phase SCIG and electrical network. The analysis employs a rotor flux vector control algorithm and a scalar strategy modulated MC to control the generator. Characteristics of MC are used for maximizing the power tracking control when different wind speeds and delivering powers to the grid are simultaneously considered. The MC provides sinusoidal input and output voltages and a unity power factor, but causes an asymmetry in the generator. A current control strategy including the method of suppressing imbalance caused by this asymmetry is discussed. Some numerical simulations are carried out showing the effectiveness of the proposed WECS topology.