Due to their superior merits over Z-source inverters, Split-Source Inverters (SSIs) has been proposed as a potential candidate for high-gain single-stage DC-AC topology. Singlestage DC-AC converters with high gains are particularly useful for interfacing PV modules with AC power grids and loads. In this study, SSI is used to interface PV modules with a singlephase grid. A simple control algorithm based on finite control set model predictive control (FCS-MPC) without needing a pulse-width modulator is presented. In this algorithm, the DClink voltage is adjusted by adjusting the grid current through the linear PI controller. Furthermore, the FCS-MPC is responsible for controlling the grid current and the input current to the SSI. The SSI input current is controlled to track the reference value determined by the MPPT algorithm. The main concept, block diagram and mathematical analysis of the proposed algorithm are presented. The system is simulated using MATLAB/Simulink to validate the proposed control algorithm. According to the simulation results, the proposed control scheme exhibits robust dynamic behaviour. Further, comparisons between analytical, modelled, and simulated responses are presented to verify the proposed algorithm.