Physical coupling, nonlinearity and uncertainty degrade the dynamic performance of electro-hydraulic servo systems, particularly under conditions involving input delays, leading to reduced trajectory tracking accuracy or even system instability. These factors often fail to meet the high-precision requirements of engineering applications. To effectively address these difficulties, this paper proposes a novel adaptive control protocol for networked electro-hydraulic servo systems. For the minimal communication delay problem of networked electro-hydraulic servo systems, Laplace transform algorithm together with Padé approximation is adopted in this study to remove the delay term from the mathematical system model. Moreover, the matched modeling parametric uncertainty of systems is estimated and compensated by the neural network adaptive method to improve the dynamical performance of the system during the steady state. The controller is designed on the basis of recursive backstepping strategy and the finite-time stability theorem, which can handle system nonlinearity and guarantee transient response. The validity of the proposed theoretical results is proved by Lyapunov stability and the feasibility and superiority are verified via physical simulation.