Safety is one of the crucial issues for robot-aided neurorehabilitation exercise. When it comes to the passive rehabilitation training for stroke patients, the existing control strategies are usually just based on position control to carry out the training, and the patient is out of the controller. However, to some extent, the patient should be taken as a "cooperator" of the training activity, and the movement speed and range of the training movement should be dynamically regulated according to the internal or external state of the subject, just as what the therapist does in clinical therapy. This research presents a novel motion control strategy for patient-centered robot-aided passive neurorehabilitation exercise from the point of the safety. The safety-motion decision-making mechanism is developed to online observe and assess the physical state of training impaired-limb and motion performances and regulate the training parameters (motion speed and training rage), ensuring the safety of the supplied rehabilitation exercise. Meanwhile, position-based impedance control is employed to realize the trajectory tracking motion with interactive compliance. Functional experiments and clinical experiments are investigated with a healthy adult and four recruited stroke patients, respectively. The two types of experimental results demonstrate that the suggested control strategy not only serves with safety-motion training but also presents rehabilitation efficacy.