This paper proposes a multiphase power generation with matrix converter for Wind Energy Conversion System (WECS). The proposed system consists of five-phase Permanent Magnet Synchronous Generator (PMSG), to generate five-phase voltage with variable amplitude and frequency. The grid is a three-phase system and hence deployment of multiphase generator needs some sort of phase conversion system. Therefore, a five-to-three phase Direct Matrix Converter (DMC) is used to interface the five-phase PMSG with the grid. The choice of multiphase machine comes from the inherent advantages of multiphase machine such as higher output power, reduced phase's losses, reduced sized for the same amount of output power compared to three phase generator. The proposed control strategy for the converter is Model Predictive Control (MPC). The proposed algorithm does the following functions: extract maximum power from the WECS, and ensures unity power factor at the grid terminal and machine terminal.