Abstract: The digital delay in the conventional linear control strategy of LCL grid-connected inverters reduces the system bandwidth and is prone to resonance instability problems under weak grid conditions with large grid inductance. For this reason, a proportional resonant-finite control set model predictive cascade control strategy（PR-MPC） is investigated in this paper. Firstly, the outer loop is kept as a proportional resonant controller to regulate the grid-connected current. Second, to reduce the control delay, a low-complexity multi-objective finite control set model predictive control（FCS-MPC） is designed for the inner loop. The intrinsic damping of the resonance is achieved by defining a bi-objective value function of capacitor voltage and inductor current. Further, the optimal inverter voltage reference is derived using the principle of minimization and an inverter voltage reference tracking value function is designed to reduce the computational complexity. Compared with the conventional active damped PR control, the proposed PR-MPC eliminates the modulation link and improves the system bandwidth and robustness under weak grid. Experimental results verify the effectiveness of the proposed PR-MPC strategy.