The serial elastic joint provides a compliant design solution for lower limb rehabilitation exoskeleton, but there are still many challenges in the design of its structure and control. Aiming at the human-robot interaction (HRI) requirements of rehabilitation exoskeletons, a series elastic joint integrated with the novel elastic element is proposed, which can realize linear/nonlinear stiffness switching subject to external loads, while achieving structural compliance. Secondly, the rigid-flexible coupling dynamic model of the modular joint is established, and a step-by-step decoupling identification of the physical system is carried out. Under the framework of model predictive control, a control algorithm is designed for nonlinear and non-convex optimization problems through an iterative linearization method. Finally, several groups of trajectory tracking experiments and disturbance experiments are conducted, and the control bandwidth of the system is discussed. Experimental results show that the proposed control method can track different reference trajectories, effectively reduce control energy consumption and suppress external disturbances under the condition of control constraints.