Continuous mode adaptation is very important and useful to satisfy the different user rehabilitation needs and improve human-robot interaction (HRI) performance for rehabilitation robots. Hence, we propose a reinforcement-learning-based optimal admittance control (RLOAC) strategy for a cable-driven rehabilitation robot (CDRR), which can realize continuous mode adaptation between passive and active working mode. To obviate the requirement of the knowledge of human and robot dynamics model, a reinforcement learning algorithm was employed to obtain the optimal admittance parameters by minimizing a cost function composed of trajectory error and human voluntary force. Secondly, the contribution weights of the cost function were modulated according to the human voluntary force, which enabled the CDRR to achieve continuous mode adaptation between passive and active working mode. Finally, simulation and experiments were conducted with 10 subjects to investigate the feasibility and effectiveness of the RLOAC strategy. The experimental results indicated that the desired performances could be obtained; further, the tracking error and energy per unit distance of the RLOAC strategy were notably lower than those of the traditional admittance control method. The RLOAC strategy is effective in improving the tracking accuracy and robot compliance. Based on its performance, we believe that the proposed RLOAC strategy has potential for use in rehabilitation robots.