Abstract This paper presents a new approach to the problem of call admission control (CAC) of variable bit rate (VBR) traffic in an asynchronous transfer mode (ATM) network. Our approach employs an integrated neural network and fuzzy controller to implement the CAC controller. This scheme capitalizes on the learning ability of a neural network and the robustness of a fuzzy controller. Experiments show that this scheme is able to achieve high throughput and low cell loss while achieving fairness among different classes of VBR traffic. For comparison, we have also implemented four other CAC schemes: (1) peak bandwidth method, (2) equivalent bandwidth method, (3) average bandwidth method and (4) neural network quality of service (QoS) predictor. Results of these experiments are presented in this paper.