The Resilient Packet Ring (RPR), standardized by the IEEE 802.17 work group, is a new topology technology for bidirectional packet-switched metropolitan backbone networks. The key objective of RPR is to achieve high bandwidth utilization, optimum spatial reuse and fairness simultaneously. Fairness algorithm is one of the core technologies of RPR. One major problem is that the bandwidth allocated by the algorithm oscillates tremendously and permanently under unbalanced traffic scenarios. So the challenge is to design a fairness algorithm in the distributed nature. This paper presented a new dynamic bandwidth allocation algorithm and the analytic results show it is effective in reducing the oscillation in RPR with low computational and time complexity.