Leakage currents represent critical issues for the operation of conventional photovoltaic (PV) inverter topologies. Recently, the common grounded (CG) PV inverter topologies have presented superior performance over the conventional PV inverter topologies from the leakage currents elimination point of view. The multilevel CG-PV inverter topologies combine both features of the multilevel output voltage and the CG connection. Among the existing CG topologies, the switched capacitor types have found wide applications due to the lower cost, volume, and losses on the passive inductors. However, burdens have been risen for the control system to achieve multi-objectives, which includes controlling the output current of the inverter and the capacitor voltages. Therefore, this paper presents a Finite Control Set Model Predictive Control (FCS-MPC) method for five-level CG single-phase PV inverter topology. The FCS-MPC method presents reduced harmonic contents of the output currents and precise tracking to its reference value. The design guidelines of the FCS-MPC method and weighting factor adjustments are provided in this paper. Simulation results are presented in order to validate the effectiveness of the FCS-MPC method.