This paper studies the synchronization control of the blanket remote maintenance robot (BRMR) of the China fusion engineering test reactor (CFETR). First, the general state space mathematical model of BRMR was established by using a physical-based method. Second, based on the receding horizon optimization of model predictive control (MPC) and cross-coupling error reduction in cross-coupling control (CCC), the innovative MPC-CCC controller was proposed to realize the single-system and multisystem error convergence and high accuracy transportation of blanket through the high accuracy synchronization control of BRMR. Third, to verify the control effectiveness of the MPC-CCC controller, two types of simulations and experiments were implied compared with the original proportional-integral (PI) controller in Mover. Results showed that simulation and experiments were highly consistent. It is found that the use of an MPC-CCC controller can result in up to a 70% reduction in displacement error and up to a 59% reduction in synchronization error compared to the PI controller. And the accuracy of the MPC-CCC controller satisfies the real requirement of the maintenance process of the blanket. This work provides the theoretical basis and practical experience for the highly stable, safe, and efficient maintenance of blankets in the future.