This research introduces an advanced finite control set model predictive current control (FCS-MPCC) specifically tailored for three-phase grid-connected inverters, with a primary focus on the suppression of common mode voltage (CMV). CMV is known for causing a range of issues, including leakage currents, electromagnetic interference (EMI), and accelerated system degradation. The proposed control strategy employs a system model that predicts the inverter's future states, enabling the selection of optimal switching states from a finite set to achieve dual objectives: precise current control and effective CMV reduction, a meticulously designed cost function evaluates the potential switching states, balancing the accuracy of current tracking against the necessity to minimize CMV. The approach is grounded in a comprehensive mathematical model that captures the dynamics of CMV within the system, and it utilizes an optimization process that functions in real-time to determine the most suitable control action at each interval, Experimental validations of the proposed FCS-MPCC scheme have demonstrated its effectiveness in significantly improving the performance and durability of three-phase grid-connected inverters, Experimental validations of the proposed (MPC with CMV) scheme have demonstrated its effectiveness in significantly improving the performance and durability of three-phase grid-connected inverters. The proposed method achieved substantial reductions in CMV, notable improvements in current tracking accuracy, and extended system lifespan compared to conventional control methods.