Model predictive control has emerged as a very powerful method for controlling of electrical energy. One of the major advantages for this control is the performance of the power converters become more better comparing with the traditional modulation control techniques. In this paper, a model predictive control is used to drive a three phase grid connected Quasi-Z-Source Inverter (qZSI) to improve the performance of the three phase injected output current. This technique uses a model of the qZSI and capacitor voltage, input inductor current and AC three phase output load currents to predict the behavior of the measured parameters. The resulting closed-loop system achieves high dynamic performance for all controlled parameters. The total system has been analyzed, simulated by using MATLAB/SIMULINK program then implement by using dSPACE 1103 to prove the idea.