Congestion in an ATM network is a condition in which performance degrades due to saturation of the network resources such as available communication links, processor speed and buffer capacity. The Connection/Call Admission Control (CAC) procedures determine if sufficient resources are available in the network to support the requested call. In this paper, a fuzzy logic based system is presented to deal with the congestion control problem in Asynchronous Transfer Mode (ATM) networks. We examine the conventional CAC and fuzzy based CAC systems. The conventional CAC systems that utilize either capacity estimation or buffer thresholds are incapable of obtaining complete statistics on input traffic. This paper exploits the fuzzy concepts in order to provide effective congestion control in ATM networks. The investigation is based on the simulation of Peak Cell Rate (PCR), Sustained Cell Rate (SCR) and Number of Calls Accepted.