Recently, Common-Ground (CG) power inverter topologies have found wide interest in photovoltaic (PV) applications. The CG topology has the ability to totally eliminate the existing leakage currents in PV systems. Among CG inverters, the multilevel CG topologies combine the benefits of CG with improved output voltage quality. The flying capacitor (FC) CG multilevel topology provides more flexibility in the selection of the FC voltage level. Therefore, this paper studies the various possible voltage levels and designs of FC-CG PV inverters. In addition, performance improvement of the flexible FC-CG PV inverter is proposed using the Finite Control Set Model Predictive Control (FCS-MPC) method. Simulation results are provided to verify that more efficient, better tracking, improved output voltage quality, and lower Total Harmonic Distortion (THD) is obtained using the proposed controller and topology design.