Scheduling policies are playing significant roles in guaranteeing the performance of core routing and switching devices. The limitations in complexities and extensibilities of current combined input and cross-point queueing switching fabric's scheduling policies are first analyzed. Then, based on this analysis, the principle for designing high extensible scheduling policies and the concept of virtual channel are proposed. Based on the principle and virtual channel, it comes up with a dynamic round robin scheduling algorithm-FDR (fair service and dynamic round robin), which is simple, and of high efficiency and fair service. FDR is based on round robin mechanism, whose complexity is only O(1). It allocates the scheduling share for each virtual channel according to its current states, thus, FDR has good dynamic and real-time performance, and it can adapt to unbalanced traffic load network environment. Simulation results under SPES (switching performance evaluation system) show that FDR exhibits good delay, throughput and anti-burst performance.