This paper presents finite-control-set modelpredictive control (FCS-MPC) for a three-phase quasi-Zsource (qZS) four-leg inverter under unbalanced load condition. The key novelty of the proposed control approach is eliminating the double-line frequency ripple in the inductor current with a simple and effective approach. The proposed four-leg qZS inverter with an output LC filter can handle buck/boost and dc/ac conversion features in a single stage. Furthermore, the FCS-MPC-based control algorithm helps in maintaining balanced point of common coupling voltages for stand-alone unbalanced loads. The behavior of the predictive controller has been investigated under different operating conditions, and its robustness with the qZS network and the LC filter parameter variations are also studied. Furthermore, the effect of double-line frequency ripple and its relation with the inductor current constraint have been tackled comprehensively. To verify the performance of the proposed approach, simulation and experimental studies were performed for balanced and unbalanced loads.