Conversion from variable ac voltage into fixed voltage and fixed frequency ac voltage is essential especially in case of grid-connected wind generation system. Direct matrix Converter (DMC) provides a solution for such ac/ac conversion for desired voltage and frequency. Five to three phase matrix converter developed in this paper is proposed to convert five-phase input voltage into three-phase voltage, control the amplitude of the output current and its frequency and also control input current power factor to be near unity with the supply voltage. Among the existing control techniques, Model Predictive Control (MPC) is considered one of the most effective control techniques. In this paper MPC is used to control the fifteen switches of the five-to-three phase matrix converters. MPC is employed to achieve the following control functions: control the output current amplitude, shape and frequency and control input current to be in phase with the supply voltage (unity power factor). The algorithm used for MPC in this paper has the advantages of no need for weighting factor. Matlab/Simulink Simulation of the proposed control system is provided including their real time validation.