In recent years, rehabilitation robots have been developed and used in rehabilitation training for patients with hemiplegia. In this paper, a rehabilitation training robot with variable damping is designed to train patients with hemiplegia to recover upper limb function. Firstly, a magnetorheological joint damper (MR joint damper) is designed for the rehabilitation training robot, and its structural design and dynamic model are tested theoretically and experimentally. Secondly, the rehabilitation robot is simplified into a spring-damping system, and the rehabilitation training controller for human movement is designed. The rehabilitation robot dynamically adjusts the excitation current according to the feedback speed and human-machine interaction torque, so that the rehabilitation robot always outputs a stable torque. The magnetorheological joint damper acts as a clutch to transmit torque safely and stably to the robot joint. Finally, the upper limb rehabilitation device is tested. The expected torque is set to 20 N, and the average value of the output expected torque during operation is 20.02 N, and the standard deviation is 0.635 N. The output torque has good stability. A fast (0.5 s) response can be achieved in response to a sudden motor speed change, and the average expected output torque is 20.38 N and the standard deviation is 0.645 N, which can still maintain the stability of the output torque.