For the problems of network delay and uncertainty in modeling the structure of the valve-controlled motor faced by the network-based hydraulic servo control system, a robust integral adaptive controller with error sign synthesized based on Pade's theorem and the backstepping derivation method was proposed. Pade's theorem was used by the controller to approximate the time delay caused by the time-varying network, and reduced the impact of the delay on the tracking performance of the control system. The adaptive rate was applied to approximate the structural uncertainty and delay error values of the system. The error sign control method was used to compensate for the remaining structural uncertainty. By constructing a suitable Lyapunov function, the global stability of the closed-loop system was verified, and the boundedness of all signals of the closed-loop system and the asymptotic convergence of the tracking error were guaranteed. The simulation results show the high-precision tracking performance of the control method.