An adaptive robust controller with non-local memory hysteresis force compensation is investigated for the precision tracking control of pneumatic artificial muscle (PAM). The proposed controller presents a two-layer cascade structure, and each layer has an adaptive law part and a robust control law part. A modified operator based Prandtl-Ishlinskii (PI) model is employed in the development of the robust control algorithm with the hysteresis feedback linearization compensation. Moreover, in the robust control law part, the problem of unbounded uncertain nonlinearities introduced by the hysteresis force term is addressed by applying an on-line monitoring method. In the adaptive law part, model parameters including weights of the modified operator are updated online by the recursive least squares estimation (RLSE) method, and then the effect of the hysteresis non-local memory characteristic is further attenuated. The tracking error is guaranteed to converge to a small residual set. Comparative experimental results demonstrate the significance of the non-local memory hysteresis force compensation, then, a desired precision can be guaranteed.