In addressing challenges such as slow parameter convergence, suboptimal tracking performance, and rigorous persistent-excitation conditions encountered in the adaptive control methods within electro-hydrostatic actuator servo system, this study explores the development of a composite learning adaptive position tracking control algorithm. Leveraging the dynamics model of the electro-hydrostatic actuator servo system, the adaptive tracking controller is formulated through a combination of backstepping control and composite learning. Notably, parameter estimation is simultaneously guided by both tracking error and prediction error, ensuring convergence of both the tracking error and parameter estimation error under interval-excitation conditions, and the consistent stability of the controller is proved by the Lyapunov theory. The simulation and experimental findings indicate that, in contrast to traditional adaptive control, the proposed method eliminates the need for a cylinder acceleration signal and demonstrating superior trajectory tracking. Following the implementation of composite learning, the system's tracking error registers a significant 50% reduction and demonstrating heightened resilience.