A connection admission control (CAC) method is proposed for asynchronous transfer mode (ATM) networks by applying the fuzzy inference and learning algorithm of neural networks. In order to guarantee the allowed cell loss ratio (CLR) in CAC, the upper bound of CLR must be used as the criterion for judging whether an incoming call can be accepted or not. For estimating the upper bound of CLR from observed CLR data, fuzzy inference, based on a weighted mean of fuzzy sets, is adopted. This inference method can effectively estimate the possibility distribution of CLR by applying the error back-propagation algorithm with the proposed energy functions in learning and provide the upper bound of CLR efficiently from the distribution. A self-compensation mechanism for estimation errors is also provided, which is simple enough to work in real time by taking advantage of the fuzzy inference method adopted. Fuzzy rules in the area with no observed data are generated by extrapolation from adjacent fuzzy rules in the area with observed data. This increases the multiplex gain, thereby guaranteeing the allowed CLR as much as possible. The simulation results show the feasibility of the proposed CAC method.