This paper proposes an adaptive control methodology using neural networks (NN) for the Available Bit Rate (ABR) service class in an ATM network. A rate-based feedback controller is developed to control traffic where sources adjust their transmission rates in response to the feedback information from the network nodes. Specifically, the ATM traffic at a given node is modeled as a nonlinear discrete-time system and a one-layer neural network controller is designed to prevent congestion. Tuning methods are provided for the NN based on the delta rule to estimate unknown traffic. Mathematical analysis is provided to demonstrate the stability of the closed-loop system so that a desired quality of service (QoS) can be guaranteed. Simulation results are provided to justify the theoretical conclusions for a single source/single node scenario.