The leaky bucket scheme is a promising method that regulates input traffic for preventive congestion control in ATM networks. One of the important problems in ATM networks is meeting the quality of service requirements for real-time and non-real-time traffics. The authors propose a priority leaky bucket scheme with queue-length-threshold scheduling policy. The motivation of this proposed leaky bucket scheme is to meet the quality of service for real-time traffic while providing more improved services for non-realtime traffic. Using the embedded Markov chain method, the authors obtain the joint distribution of the queue lengths, the loss probability and the mean waiting time. Numerical results show the effects of the system parameters such as the buffer size and the token pool size on the performance of the proposed scheme.