The capacitive-coupling grid-connected inverter (CGCI) is coupled to the point of common coupling via a second-order LC branch. Its operational voltage is much lower than that of a conventional inductive-coupling grid-connected inverter (IGCI) when it serves as a multifunctional inverter to compensate reactive power and transfer active power simultaneously. It is a promising solution for microgrid and building-integrated distributed generator systems. A quasi-proportional-resonant (quasi-PR) controller is applied to reduce the steady-state current tracking errors of the CGCI in this paper. The quasi-PR controller generates the voltage reference for use of carrier-based pulse-width modulation, which can effectively reduce output current ripples. The second-order coupling impedance of the CGCI causes its modeling and controller design to differ from that of the conventional IGCI. A comprehensive design method for the quasi-PR controller in a CGCI is developed. The quasi-PR controller is also compared with a proportional-integration current controller. Simulation results are provided to verify the effectiveness of the quasi-PR controller and its design method in a CGCI. The current tracking errors are greatly reduced when the quasi-PR controller rather than the proportional-integration controller is applied. Experimental results are also provided to validate the CGCI as a multifunctional grid-connected inverter.