This paper presents a single phase seven-level inverter grid connected photovoltaic (PV) system application. The proposed system consists of a PV arrays, a single phase seven-level inverter interface and single phase power grid. The control of the inverter is based on a model predictive control algorithm where the main aim is to control the injected power which is produced by the PV source, to improve the quality of the current waveform, to reduce the THD of the current and to ensure the elimination of the shift phase between the injected current and the grid voltage in order to fulfill the requirement of the smart grid network. To clarify the advantages of the application of the model predictive control to the proposed topology, simulation results using MATLAB/SIMULINK and real time simulations using dSPACE 1103 are provided in this paper.