In the rate-based congestion control, three distinct schemes - Explicit Forward Congestion Indication (EFCI), Backward Explicit Congestion Notification (BECN), and Explicit rate based scheme - are mixed within the ATM Forum. With respect to implementation complexity, the EFCI or BECN are better than the explicit rate based scheme. In this paper, we propose an Enhanced BECN scheme to support max-min fairness problem and a method to determine the optimal source recovery time and filter period in order to minimize the maximum queue length and improve the link utilization. Especially the minimization of queue length fluctuation gives better performance over cell delay variation, end-to-end delay, and so on. Moreover the max-min fairness can be guaranteed with simple use of Resource Management (RM) cells containing Current Cell Rate generated by Source-End-Systems without increasing implementation complexity of the switch.