A complete control strategy is proposed for the bi-directional isolated AC/DC matrix converter, the pulse width modulation method based on the fitting of maximum input voltage is adopted in the front-end converter, and a control method similar to synchronous rectification is adopted in the back-end H-bridge circuit. The simulation results show that in both rectifier and inverter mode the sinusoidal grid current and unity power factor are realized, and the output current keeps constant with less than 3% ripple, which demonstrate the validity and efficiency of the proposed control strategy.