In this paper, a five-leg topology structure of the unified power quality conditioner (UPQC) is proposed to realize comprehensive compensation of power quality disturbances in fault-tolerant mode. The series converter and parallel converter are modeled uniformly, and a control strategy of five-leg UPQC based on finite control set model predictive control (FCS-MPC) is proposed. Compared with traditional linear control strategy, the proposed algorithm constructs a unified prediction model and integrates the optimized cost function to realize the cooperative control of series and parallel converters. In addition, the compensation accuracy, transient performance and response speed of the converters on both sides are improved. The complexity of the control algorithm and the difficulty of parameter adjustment are effectively reduced with high parameter robustness. Simulation results verify the feasibility and effectiveness of the proposed algorithm. This work is supported by the National Natural Science Foundation of China (No. 51807139 and No. 51977149).