A new integral sliding mode control strategy for high-speed networks operating in asynchronous transfer mode (ATM) is derived to cope with the congestion problem in network flow control. The novelty of the proposed design solution stem from allowing high-speed networks to have simultaneously acting multiple time-varying input delays, uncertainties and time-varying perturbations. A delay-dependent condition is derived via the linear matrix inequality approach that guarantees both the asymptotic stability and a prescribed H-performance level of the closed-loop system in sliding mode dynamics when perturbations of available bit-rate bandwidth occur. These new results are obtained with no restriction on the derivative of the time-varying delays hence are less conservative than the existing ones. This control scheme does achieve both of the main goals in ATM network traffic, namely convergence of the queue length to the desired steady-state status and the weighted fairness condition. The application to benchmark bottleneck example and the simulation results demonstrate the applicability, efficiency and robustness of the proposed synthesis method.