In this paper, a Novel Compliant Actuator (NCA)-driven Upper-Limb Exoskeleton (ULE) with force controllable, impact resistance, and back drivability is designed to ensure the safety of the subject during Human-Robot Interaction (HRI) processing. Based on the designed NCA-driven ULE, this paper constructs a Model Predictive Control Scheme (MPCS) for force trajectory tracking, which minimises future tracking errors by solving an optimal control problem with inequality constraints. In addition, an Error-Accumulation Improved Newton Algorithm (EAINA) is proposed to solve the MPCS for suppressing various noises and external disturbances. The proposed EAINA is theoretically proved to have small steady state for noise conditions and stability of the EAINA using Lyapunov method. Finally, experimental results verify that the proposed MPCS solved by the EAINA in the NCA-driven ULE achieves robustness, fast convergence, strong tolerance and stability for trajectory rehabilitation task.