This paper addresses the load voltage tracking and current stabilizing problem in a three-phase unified power quality conditioner (UPQC) system under multiple disturbances (including harmonic disturbances brought by nonlinear loads and perturbations caused by grid voltage sags and swells). A composite disturbance observer is designed to estimate the multiple mismatched disturbances with the presence of various types of loads and different power quality issues. Based on the disturbance estimation, a composite-disturbance-observer-based MPC (CDOB-MPC) controller is proposed to implement complex and unified effect on both series filter and shunt filter of UPQC. The proposed controller is capable of addressing disturbance attenuation and grid voltage compensation problems simultaneously, improving the dynamic and steady-state performance of UPQC. Simulations are carried out to verify the effectiveness of the proposed control strategy. Based on the presented results, the proposed control algorithm achieves fast convergence velocity, good disturbance rejection capability and maintains small tracking error.