Abstract: The switched-inductance quasi-Z-source inverter can improve the reliability and energy conversion efficiency of photovoltaic power generation system,however,its finite control set model predictive control（FCS-MPC）has multiple control variables and difficult to adjust the weight coefficients. This paper proposes a photovoltaic off-grid switched-inductance quasi-Z-source inverter model predictive control strategy based on multi-objective optimization ranking. Firstly,the state of the next control cycle is judged based on the predicted value of inductor current,and if it is a non-through state,the cost functions of load current and capacitor voltage are calculated separately and sorted in the order from smallest to largest,and then the two sorted values are summed to obtain the sorted sum,and the switching state corresponding to the smallest sorted sum will be applied to the switching state of the next cycle of the inverter,which effectively eliminates the weighting factor of the traditional FCS-MPC strategy. Simulation analysis and experimental results show that the proposed control strategy has good steady and dynamic characteristics.