The electro-hydrostatic actuator (EHA), the actuator of electric drive and hydraulic transmission, is competitive since it is small in size, light in weight and high in power density. However, the existence of the velocity loop error of servo motors, unmodeled dynamics and highly nonlinear uncertainties restrict the improvement of the tracking accuracy of the EHA system. In order to achieve high-precision motion control of EHAs, a RISE-based composite adaptive control scheme is proposed in this paper. In the proposed composite adaptive control design, a novel parameter adaptive law is synthesized to compensate for the parametric uncertainties and a robust integral of the sign of error (RISE) feedback is utilized to suppress the adverse effects caused by the lumped disturbances, including the velocity loop error of a servo motor and other unmodeled dynamics. The synthesized parameter adaptive law possesses the advantage of fast convergence, which is beneficial to achieve transient tracking performance improvement. In addition, the proposed controller is more suitable for practical applications since it is chattering free. The closed-loop system stability analysis shows that the proposed control scheme guarantees an excellent asymptotic tracking performance. Finally, comparative simulations are conducted to verify the high-performance nature of the proposed controller.