This paper presents the computer simulation model of a grid to vehicle (G2V) wireless power supply using a single-phase matrix converter (SPMC). The proposed system uses the SPMC that operates as a direct AC-AC converter to convert the supply frequency of 50 Hz to reach 20 kHz output frequency. The use of 20 kHz frequency is suitable for wireless power transfer (WPT) operation in order to obtain higher power transfer efficiency between the transmitter and the receiver parts. An advanced of the proposed circuit topology can solve the conventional system for G2V circuit topology that uses multiple stages of power conversion system, resulting in high power semiconductor losses that could lead to low efficiency. In this work, multiple stages of the conventional "AC-DC-AC" circuits have been reduced to a single power conversion stage by using the SPMC circuit topology. The use of the proposed circuit topology can reduce the number of devices, thus reduce the semiconductor losses. A part of reducing the semiconductor losses, the proposed circuit topology could also improve the power density and efficiency of the power supply system. A computer simulation model using MATLAB/Simulink has been developed to investigate the behavior of the proposed system. Selected simulation results are presented to verify the functionality of the proposed system.