The Gauranteed Frame Rate service category was proposed by the ATM Forum as an enhancement to the UBR service. This service aims to support minimum cell rate gaurantee for each virtual connection and allow any excess bandwidth in the network to be shared among the contending VCs in a fair manner. We propose a new buffer management algorithm for GFR service through FIFO queuing discipline. Proposed scheme can provide minimum bandwidth guarantee for GFR VCs as well as improve the fairness among the competing GFR VCs on a single FIFO queue. From simulation results, we demonstrate the proposed scheme fulfills the requirement of GFR service as well as improves the TCP throughput.