This paper presents a model predictive control (MPC) of five-level H-bridge neutral-point-clamped (NPC) quasi-impedance source inverter (qZSI). The proposed control technique is designed to handle three control objectives with simple and effective approach. The output current, the input current and the capacitor voltage are the control objectives of the proposed MPC algorithm. To fulfill these control objectives, multi-objective based cost function is employed. Furthermore, qZSI has been combined with the 5-Level H-bridge NPC inverter so as to obtain power converter topology with buck/boost and dc/ac conversion functionality in a single stage for high power PV applications. Simulation results verily the proposed multi objective MPC algorithm and inverter topology.