The existing buffer management scheme is caused by with burstness characteristic of the TCP traffic and with only the transmission which is not loss it provides the smallest transmission rate guarantee where the GFR demands and a fair characteristic. In order to provide a high fair characteristic from the dissertation which it sees with the smallest transmission rate guarantee where the GFR demands it proposed the existing buffer algorithm which applies a Fuzzy mechanism in the existing buffer management technique. The proposed algorithm decides a packet disuse used by three parameters which are composed of tagging information, the buffer usage, and the load of VC. Simulation results shows that the fairness and goodput of the proposed algorithm were excellent where the size of MCR will become larger, from the switch the Double-EPD or the DFBA was visible a similar efficiency even from size change of the buffer. The algorithm which is proposed provides a good throughput and a fair characteristic.