The current source inverter (CSI) is a promising interface between the Photovoltaic (PV) panel and the three-phase AC grid. It boosts the PV panel voltage by a DC-link inductor and converts the maximum available PV power. In an unbalanced grid, double-line-frequency pulsating powers will be generated in the CSI, increasing the rating of the DC-link inductor and impeding the maximum power point tracking (MPPT) operation. To address this issue, a power decoupling (PD) circuit for a three-phase CSI is proposed in this paper. By using the DC-link inductor and active switches multiplex, the proposed PD circuit can reduce the current rating of the DC-link inductor with fewer active switches, and no detrimental power components are introduced to the utility grid. Moreover, to concurrently control multiple objectives without multiple loops, a model predictive control (MPC) method is further proposed for the PD-CSI, achieving a rapid response of PD-CSI. Besides, a space vector pulse width modulation (SVPWM) method is proposed for the PD-CSI to enhance the utilization of DC voltage, helping to reduce the voltage stress of the ripple storage capacitor. The priorities of the proposed topology and the corresponding control and modulation methods are finally verified by comparative experimental results.