Most recent studies on adaptive hydraulic tracking control focus on trajectory tracking performance while the parameter convergence property is often unsatisfying. This paper proposes a composite learning adaptive position tracking controller with improved parameter convergence for electro-hydraulic servo systems. In the composite learning, a prediction error is formulated to exploit input-output memory data, and parameter estimates are driven simultaneously by tracking and prediction errors. Practical exponential stability of the closed-loop system, which implies the convergence of both the tracking and parameter estimation error, is established by a more realizable interval-excitation condition than the stringent persistent-excitation condition. Therefore, superior trajectory tracking is obtained compared with the classical adaptive hydraulic control. Besides, the initial fluid control volumes of hydraulic systems are assumed to be unknown a priori, which enhances the generality of the proposed control approach. The above two properties are generally not achievable in prevalent approaches to adaptive hydraulic control. Moreover, noisy acceleration signals and the time derivatives of pressure signals are not needed in the proposed approach, which improves its robustness against measurement noise. Extensive experimental results verify its superiority over currently available ones.