Abstract: The statistical multiplexing of sources with diverse traffic characteristics in ATM networks necessitates the use of some policing mechanisms, especially sources with bursty traffic characteristics. Because of the statistical nature of burstiness, the policing of these sources is difficult and the known policing mechanisms cannot control them effectively. Even the leaky bucket control mechanism, which is the most widely and only implemented one has some drawbacks. Although the Buffered-Learning Leaky Bucket (BLLB) shows nice improvements over the Leaky Bucket, yet the harshness of its decision might slow down the increase in the performance. In this paper a fuzzy approach for the BLLB aiming to overcome the uncertainty of the sources is proposed. This will relax the limits that BLLB suffered from. Simulation results show that the proposed Fuzzy Buffered Learning Leaky Bucket (FBLLB) can achieve superior system utilization compared to Leaky Bucket and BLLB. It results in high learning speed, and simple design procedure, while increasing the level of QoS.