A simple and economical upper-limb exoskeleton robot actuated by the pneumatic muscle is developed. Aiming at the problem of large tracking error, poor robustness, and chatter in single pneumatic muscle joint motion control, a backstepping method based adaptive robust controller is developed. This controller presents a two-layer cascade structure, and each layer includes a robust feedback part, a recursive least squares estimation based parameter adaptive part, and a gradient-based fast dynamic compensation term. The controller stability is proven by the Lyapunov theory, and the effects of the parameter adaptive and fast dynamic compensation term are analyzed further in terms of the comparative experiments. The results validate the excellent transient and steady performance of the developed controller, especially the transient absolute tracking error is less than 0.94 mm and the steady-state root-mean-square tracking error is less than 0.21 mm during tracking sinusoidal signal with an amplitude of 15 mm. Furthermore, disturbance experiments validate the developed adaptive robust controller inherits the disturbance objection ability from the deterministic robust controller.