With unique advantages in flexibility, adaptability, and safety, pneumatic artificial muscle (PAM) has been widely applied in fields such as rehabilitation medical robots and soft robotic arms. This paper develops a PAM-driven lower-limb exoskeleton robot for lower-limb motor rehabilitation. Due to inherent characteristics of PAMs, such as parameter disturbances and hysteresis effects, a magnetorheological damper (MRB) with real-time adjustable damping characteristics is introduced in this study to enhance the motion stability of the PAM-driven rehabilitation robot. Furthermore, an input-output constrained adaptive neural network control method suitable for flexible joint robots is proposed. To verify the effectiveness of the proposed control algorithm on the PAM-driven rehabilitation robot, a series of experiments were conducted on a self-built exoskeleton robot. Compared with the classical PID control, this method can track the desired trajectory faster, and the tracking accuracy gradually improves.