In this paper, we show the movable boundary (MB) method is the effective bandwidth allocation strategy for the ABR service among existing bandwidth allocation methods. The MB method can gurantee the QOS requirement according to the service priority and improve bandwidth utilization using the characteristics of the ABR service. The threshold values of the MB, which have an important effect upon connection blocking probability(CBP) performance of each service, are obtained by simulation. The MB method with the fixed thresholds, however, may not have good performance to variation of input traffic parameters. We suggest the dynamic MB method which changes the threshold values adaptively according to the required bandwidth of input traffic. We also show that the dynamic MB method can urantee the CBP performance according to the service priority regardless of variation of input traffic parameters.