Transformerless grid-connected solar photovoltaic (PV) systems have given rise to more research and commercial interests due to their multiple merits, e.g., low leakage current and small size. In this paper, a model-predictive-control (MPC)-based strategy for controlling transformerless H5 inverter for single-phase PV distributed generation system is proposed. The method further reduces the PV leakage current in a cost-effective and safe manner and it shows a satisfactory fault-ride-through capability. Moreover, for the first of its kind, PV maximum power point tracking is implemented in the single-stage H5 inverter using MPC-based controllers. Various case studies are carried out, which provide the result comparisons between the proposed and conventional control methods and verify the promising performance of the proposed method.