Using a rehabilitation robot to activate motion intention and reflex response simultaneously is an effective approach to aiding recovery from paralysis caused by neurological disorders. Mechanical motions supported by conventional robots are, however, not enough to activate reflex. In this paper, we propose a grasp-training robot that can stimulate the grasp reflex of a paralyzed hand by pushing the hand onto an elastic bar while supporting the grasping movements. In addition to this feature, we discuss the robot design in relation to its usability and wearability for ease of use in clinical practice. Experimental results obtained from healthy subjects show that the proposed robot can support grasping in a way similar to the traditional range-of-motion exercise used by therapists for grasp rehabilitation. Combining this appropriate grasping-motion support and the mechanism for pushing the hand onto an elastic bar succeeds in activating the grasp reflex of a completely paralyzed patient in a clinical test that involves monitoring electromyography signals from the paralyzed hand.