In order to improve the adaptability and fairness of RED, we replace the buffer occupancy of individual flow with a new introduced variable - Sharing Index to indicate the network resource share among difference flows. Through defining linguistic rules of both Sharing Index and queue length, a fuzzy logic based buffer management algorithm named FF-RED is proposed. When calculating packet dropping probability in FF-RED algorithm, the probability will further increase or decrease based on the sharing of network resource, so it can make use of the difference between flows to make congestion relief more quickly, and it is more fair and has better adaptability.