A pneumatic artificial muscle (PAM) actuated robot is developed for the elbow joint rehabilitation and assisted movement of the arm in this paper. The PAM utilized has the characteristics of flexible actuation, making it user-friendly and safe during the user-robot collaboration. However, its hysteresis nonlinearity significantly affects the motion accuracy of the robot. Offline parameter identification and model inversion are the two main steps of common model-based hysteresis compensation strategies, whereas the robustness against the variation of the system's configuration is low. This paper presents a hysteresis compensation strategy based on the direct inverse modeling method and a modified adaptive projection algorithm. The inverse PI model is adopted as the hysteresis compensator, and a modified adaptive projection algorithm is utilized to adjust the parameters of the inverse PI model online. It has been verified by experiments that the proposed method is effective in hysteresis compensation, and the transient performance of the system has been improved. In the meantime, the performance of the closed-loop system on tracking different types of trajectories is experimentally tested.