In this article, a robust trajectory tracking control method is proposed for the passive gait training exoskeleton system driven by pneumatic muscles (PMs). Conventional model-based controllers suffer from limitations with respect to model uncertainties and external disturbances caused by PMs and complex robotic systems. An echo state network (ESN) is used in this study to approximate the model uncertainties and external disturbances of the exoskeleton system. Based on the approximation of ESN, a super-twisting control (STC) algorithm is designed to guarantee accurate tracking control at both hip and knee joint levels. Because there are both weight error and global approximation error in neural network approximation, a standard quadratic form cannot be obtained which plays an important role in the stability analysis of the traditional super twisting algorithm. To solve this issue, a dedicated positive definite matrix is constructed in this article, which bridges the ESN and STC by providing a parameter selection criteria. The stability with respect to the tracking problem of the exoskeleton system is then guaranteed according to the Lyapunov theorem. Both numerical simulations and experimental results present better tracking accuracy and robustness compared with the traditional sliding mode control and STC.