The Resilient Packet Ring (RPR), defined under IEEE 802.17 , has been proposed as a high-speed backbone technology for metropolitan area networks. RPR is introduced to mitigate the underutilization and unfairness problems associated with the current technologies SONET and Ethernet, respectively. The key performance objectives of RPR are to achieve high bandwidth utilization, optimum spatial reuse on the dual rings, and fairness. The challenge is to design an algorithm that can react dynamically to the traffics in achieving these objectives. The RPR fairness algorithm  is comparatively simple, but it poses some critical limitations that require further investigation and remedy. One of the major problems is that the amount of bandwidth allocated by the algorithm oscillates severely under unbalanced traffic scenarios. These oscillations are barrier to achieving spatial reuse and high bandwidth utilization. In this paper, we propose a Low Complexity Fairness Algorithm (LCFA) to allocate bandwidth fairly to RPR nodes with a very low computational complexity O(1) that requires a simple hardware requirement similar to that of the RPR fairness algorithm.