The explicit rate flow control mechanisms for ABR service are used to sharethe available bandwidth of a bottleneck link fairly and reasonably among many competitive users andto maintain the buffer queue length of a bottleneck switch connected to the link at a desired levelin order to avoid and control congestion in ATM networks. However, designing effective flow controlmechanisms for the service is known to be difficult because of the variety of dynamic parametersinvolved such as available link bandwidth, burst of the traffic, the distances between ABR sourcesand switches. In this paper, we present a fuzzy explicit rate flow control mechanism for ABRservice. The mechanism has a simple structure and is robust in the sense that the mechanism'sstability is not sensitive to the change in the number of active virtual connections (VCs). Manysimulations show that this mechanism can not only effectively avoid network congestion, but alsoensure fair share of the bandwidth for all active VCs regardless of the number of hops theytraverse. Additionally, it has the advantages of fast convergence, low oscillation, and high linkbandwidth utilization.