This paper presents an improved current control strategy for a three-phase grid-connected inverter under distorted grid conditions. In terms of performance, it is important for a grid-connected inverter to maintain the harmonic contents of inverter output currents below the specified limit even when the grid is subject to harmonic distortion. To address this problem, this paper proposes a modulated finite control set-model predictive control (FCS-MPC) scheme, which effectively mitigates the harmonic components in output current of a grid-connected inverter. In the proposed scheme, the system behavior in the future is predicted from the system model in the discrete-time domain. Then, the cost function is selected based on the control objective of system. This cost function is minimized during the optimization process to determine the control signals that minimize the cost function. In addition, since the proposed scheme requires pure sinusoidal reference currents in the stationary frame to work successfully, the moving average filter (MAF) is employed to enhance the performance of the traditional phase lock loop (PLL). Due to the control performance of the FCS-MPC scheme as well as the harmonic disturbance rejection capability of the MAF-PLL, the proposed scheme is able to suppress the harmonic distortion even in the presence of distorted grid condition, while retaining fast transient response. Comparative simulation results of different controllers verify the effectiveness of the proposed control scheme in compensating the harmonic disturbance. To validate the practical feasibility of the proposed scheme, the whole control algorithm is implemented on a 32-bit floating-point digital signal processor (DSP) TMS320F28335 to control a 2 kW three-phase grid-connected inverter. As a result, the proposed scheme is a promising approach toward improving the current quality of a grid-connected inverter under distorted grid conditions.