This paper presents a finite-control-set model predictive control (FCS-MPC) for grid-tied packed U cells (PUC) multilevel inverter (MLI). The system under study consists of a single-phase 3-cells PUC inverter connected to the grid through filtering inductor. The proposed competitive topology allows the generation of 7-level output voltage with reduction of passive and active components compared to the conventional MLIs. The aim of the proposed FCS-MPC technique is to achieve, under various operating conditions, grid-tied current injection with unity power factor and low total harmonic distortion while balancing the capacitor voltage. Parameters' sensitivity analysis was also conducted. The study is conducted on a low-power case study single-phase 3-cells PUC inverter and with possible extension to higher number of cells. Theoretical analysis, simulation, and experimental results are presented and compared.