This paper presents a Model Predictive Control (MPC) for grid-tied Packed U Cells (PUC) multilevel inverter. The system under study consists of a single-phase 3-cell PUC inverter connected to the grid through filtering inductor. The proposed topology allows the generation of 7-level output voltage with reduction of passive and active components compared to the conventional multilevel inverters. The aim of the proposed MPC technique is to achieve grid-tied current injection, low Total Harmonic Distortion (THD) of the current, unity power factor, while balancing the capacitor voltages at maximum power point (MPP). The feasibility of this strategy is validated by simulation using Matlab/Simulink environment.