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Owing to variable stiffness, natural compliance, and similarities with skeletal muscles, pneumatic artificial muscles (PAMs) have been widely utilized in the fields of bionic robots, medical rehabilitation, and industrial manufacturing. However, in addition to high nonlinearities, time variation, and uncertainties, PAMs are extremely sensitive to external disturbances in practical applications, most of which are unknown, complicated, and constantly changing. Regarding these challenging issues, a disturbance compensation-based robust control method is proposed in this paper, which realizes satisfactory tracking control of PAM systems without a prior knowledge of exact models. Particularly, without assuming that disturbances or their first-order derivatives are invariable, a high-order disturbance observer is proposed to estimate lumped disturbances and their nth-order derivatives. On this basis, a nonlinear feedback controller is designed to simultaneously ensure that the observation errors converge to zero in finite time and the tracking error converges to zero asymptotically. Further, based on Lyapunov techniques, the stability analysis for the equilibrium point of the closed-loop system is provided in detail. Finally, the practicability and the robustness of the proposed method are validated by hardware experiments on a self-built horizontal PAM platform.