In order to improve the dynamic response speed and reduce the switching frequency of the single-phase quasi-Z-source cascaded multilevel inverter (qZS-CMI), an optimized finite set-model predictive control (FCS-MPC) strategy is proposed. Firstly, the influence of different operations on qZS-CMI state variables is analyzed to establish the discrete time model. Secondly, according to the established discrete time model and the input current reference from MPPT, the input current, output capacitor voltage and load current of the quasi-Z-source network are predicted and introduced into the cost function to achieve multi-variable comprehensive collaborative control of qZS-CMI system. Then, the average switching times are introduced into the cost function to optimize the switching loss of the system. The proposed model predictive control method can reduce the difficulty of adjusting control parameters and improve the dynamic response speed of the system without the output current control loop and the DC side voltage control loop. Finally, the effectiveness and correctness of the proposed algorithm are verified by the simulation model. This work is supported by National Natural Science Foundation of China (No.51707126).