Single-phase PWM Voltage-Source Inverters are widely employed for Photovoltaic (PV) grid connected systems. Since the voltage at the Point of Common Coupling (PCC) is regulated by the grid, the current control strategy of the grid-connected inverters play a dominant role in providing high power quality for the grid. This paper presents a novel deadbeat current controller for single phase PV grid connected inverters. This control method uses discrete-time model of the system in order to produce the inverter voltage for reaching the current reference. In comparison with earlier works, the resistance between the inverter and the grid is modeled in the proposed controller, which improves the controller performance. Despite a more accurate model, the controller is simplified; thus, the implementation is simpler. The proposed controller is applied to the H-Bridge inverter along with the unipolar modulation. Simulation results validate the controller performance in different conditions including current reference tracking, grid variations, and line filter tolerances.