Resilient packet ring (RPR), defined under IEEE 802.17, is a new kind of metropolitan area network technology. Fairness algorithm is one key technology of RPR. Presently, fairness algorithms found in RPR draft and related publications (e.g., DVSR algorithm) have some critical and common limitations, such as oscillation of the allocated bandwidth, high computation complexity or not get high bandwidth utilization. In this paper, we propose a new GPS-based algorithm, FBDRR algorithm, with a view to overcome these limitations. GPS is an ideal scheduling algorithm that can fairly allocate bandwidth to different flows and can also isolate vicious users. Its principle is that when downstream has high demand and make network congested and lost some frames, the low demand traffic from upstream node will has the same loss rate with the downstream one, and if one node does not constrain its stream to its fair share bandwidth, then it can use all of the bandwidth for C class if ring priority scheduling algorithm is used. We analyze the stability of this algorithm. Theoretical analysis and simulation results demonstrate that with this fairness algorithm, each node on the ring can remotely approximate the ideal fair rate for its own traffic at each downstream link, and there is no permanent oscillation, i.e., satisfied stability.