In the current ATM AAL5 implementation, even a single cell loss event can lead to the corruption of one whole packet. Hence, it has been observed that the throughput of upper layer protocol may easily collapse on a congested ATM network. In this paper, we propose a buffer management method called Age Priority Packet Discarding (APPD) scheme to be used along with two other schemes: the Early Packet Discarding (EPD) and the Partial Packet Discarding (PPD) schemes. After describing the operations and the pseudo code of the proposed APPD scheme and how it operates with the EPD/PPD schemes, the packet level QoS of APPD and its extended versions are derived analytically under homogeneous ON-OFF source model. Numerical results obtained via analytical approach suggest that the proposed APPD scheme can more effectively and fairly reduce packet loss probability than other schemes.