WFQ (Weighted Fair Queuing) provides not only fairness among traffic flows in using bandwidth but also guarantees the Quality of Service (QoS) that individual flow requires, which is why it has been applied to the resource reservation protocol (RSVP)-capable router. The RSVP allocates an enough resource to satisfy both the rate and end-to-end delay requirements of the flow in the condition of no packet loss, and the WFQ scheduler guarantees those QoS requirements with the allocated resource. In practice, however, most QoS-guaranteed services allow a degree of packet loss, especially from 0.1% to 3% for Voice over IP. This paper discovers that the packet loss rate of each traffic flow is determined by only its time-stamp adjustment value, and then enhances the WFQ to provide a differentiated packet loss guarantee under general traffic conditions in terms of both traffic characteristics and QoS requirements. The performance evaluation showed that the proposed WFQ could increase the utilization of bandwidth by 8~11%.