Broadband ISDN, using asynchronous transfer mode, are expected to carry traffic of different classes, each with its own set of traffic characteristics and performance requirements. To achieve the quality of service in ATM networks, a suitable buffer management scheme is needed. In this paper, we propose a buffer management scheme using a priority service discipline to improve the delay time of delay-sensitive class and the packet loss ratio of loss-sensitive class. The proposed priority scheme requires simple buffer management logic and minor processing overhead. We also analyze the delay time and the packet loss ratio for each class of service. The results indicate that the required buffer size of the proposed priority scheme is reduced and the delay time of each class of service is controlled by a parameter. If the control parameter is appropriately chosen, the quality of service of each class is improved.