A low-pass filter (LPF) for ATM traffic measurement is presented and an admission control method based on it is proposed. Instantaneous rate is estimated with the LPF and the maximum instantaneous rate (MIR) observed over the monitoring period is used to determine the residual bandwidth in the method. Hence we call it the MIR method. We developed an analytical model to investigate the performance of the MIR method. We confirmed that the MIR method regulates the number of connections properly even for connections with long holding time. In addition, the MIR method is robust against long range dependent traffic, which degrades the robustness of many previously proposed methods. Because the MIR method does not assume any mathematical model and can be implemented with simple hardware, it is well suited for practical ATM switching systems.