Conventional lower limb exoskeletons (LLEs) and their corresponding rehabilitation protocols can hardly provide safe and customizable gait rehabilitation training for different patients and scenarios. Thus, this study presents an 8-DoF rehabilitation LLE equipped with a cable-driven body weight support (BWS) mobile mechanism. The mobile BWS mechanism is designed to follow the wearer and offer preset supportive forces and balance protection. A whole body motion planning approach is proposed, wherein iterative null-space projection is employed to solve the task-space trajectories of gait training into the joint-space trajectories of the LLE. For better control performance, dynamic parameters of the human-LLE coupling system are estimated. A control scheme combining robust model predictive control (MPC) and disturbance observer is then designed to manipulate the system against dynamics uncertainty and disturbance during trajectory tracking. In the validation experiments, the nominal model of robust MPC is discretized into quadratic programming problems and solved online by the neuro-dynamics optimization. The experimental results demonstrate the rationality of our system design and motion planning method as well as the effectiveness and stability of the control scheme.