Because of system constraints caused by the external environment and grid faults, the conventional maximum power point tracking (MPPT) and inverter control methods of a PV power generation system cannot achieve optimal power output. They can also lead to misjudgments and poor dynamic performance. To address these issues, this paper proposes a new MPPT method of PV modules based on model predictive control (MPC) and a finite control set model predictive current control (FCS-MPCC) of an inverter. Using the identification model of PV arrays, the module-based MPC controller is designed, and maximum output power is achieved by coordinating the optimal combination of spectral wavelength and module temperature. An FCS-MPCC algorithm is then designed to predict the inverter current under different voltage vectors, the optimal voltage vector is selected according to the optimal value function, and the corresponding optimal switching state is applied to power semiconductor devices of the inverter. The MPPT performance of the MPC controller and the responses of the inverter under different constraints are verified, and the steady-state and dynamic control effects of the inverter using FCS-MPCC are compared with the traditional feedforward decoupling PI control in Matlab/Simulink. The results show that MPC has better tracking performance under constraints, and the system has faster and more accurate dynamic response and flexibility than conventional PI control.