In this paper, we suggested a method for evaluating the type-I/II error which is proposed by the CCITT as a criterion for the accuracy of policing algorithms in ATM networks, By the analysis of the type-I/II error of the Leaky Bucket(LB) algorithm, we investigated the relationships between the traffic parameters and the LB parameters to police the mean and peak cell rate effectively in the ON/OFF traffic. We showed that the LB parameters, the leaky rate a and the threshold M of the LB counter, could be determined as a pair of (a, M) satisfying the type-I/II error and minimizing the response time. In the ON/OFF traffic, it has been observed that the a-M characteristic curve of the LB policing algorithm only depends on the burstiness. As the results of the performance analysis, we found that the LB algorithm exhibits a good performance in the peak rate policing, but has some problems in the mean rate policing due to the trade-off between the accuracy and the response time.