The tuning of weighting factor has been considered as the most challenging task in the implementation of multi-objective model predictive control (MPC) techniques. Thus, this paper proposes an artificial intelligence (AI)-based weighting factor autotuning in the design of a finite control set MPC (FCS-MPC) applied to a grid-tied seven-level packed U-cell (PUC7) multilevel inverter (MLI). The studied topology is capable of producing a seven-level output voltage waveform and inject sinusoidal current to the grid with high power quality while using a reduced number of components. The proposed cost function optimization algorithm ensures auto-adjustment of the weighting factor to guarantee low injected grid current total harmonic distortion (THD) at different power ratings while balancing the capacitor voltage. The optimal weighting factor value is selected at each sampling time to guarantee a stable operation of the PUC inverter with high power quality. The weighting factor selection is performed using an artificial neural network (ANN) based on the measured injected grid current. Simulation and experimental results are presented to show the high performance of the proposed strategy in handling multi-objective control problems.