The leaky bucket scheme is a promising method that regulates input traffics for preventive congestion control. In the ATM network, the input traffics are bursty and transmitted at high-speed. In order to get the low loss probability for bursty input traffics, it is known that the leaky bucket scheme with static leaky rate requires larger data buffer and token pool size. This causes the increase of the mean waiting time for an input traffic to pass the policing function, which would be inappropriate for real time traffics such as voice and video. We present the leaky bucket scheme with dynamic leaky rate in which the token generation period changes according to buffer occupancy. In the leaky bucket scheme with dynamic leaky rate, the cell loss probability and the mean waiting time are reduced in comparison with the leaky bucket scheme with static leaky rate. We analyze the performance of the proposed leaky bucket scheme in discrete-time case by assuming arrival process to be Markov-modulated Bernoulli process (MMBP).