The capacitive-coupling grid-connected inverter (CGCI) is able to achieve reactive power compensation and active power transfer simultaneously with a low operational voltage. The CGCI is coupled to the point of common coupling (PCC) via a second-order LC circuit, which makes its modeling and current control characteristics differs from the conventional inductive-coupling grid-connected inverter. The direct current tracking with hysteresis pulse width modulation (PWM) was used in previous studies. However, this method suffers from widely varying switching frequency and large current ripples. A Quasi-proportional-resonant (Quasi-PR) current controller is designed for the CGCI in this paper. Its modeling and parameter selection are studied in detail. In contrast with proportional-integration (PI) current controller, the Quasi-PR controller reduces steady-state error. It also generates a voltage reference for applying the carrier-based PWM to improve output waveform quality. Simulation results are provided to verify the Quasi-PR controller and comparison with the PI controller is also done. A lab-scale prototype is built. Experimental results are given to show the validity of the proposed control method and its design.