Guaranteed Frame Rate (GFR) service category is one of the most recent ATM service categories. The GFR specification was recently finalized by the ATM Forum and is expected to become an important service category which can efficiently support TCP/IP traffic in ATM network. In GFR switch implementation, it is important to guarantee MCR (minimum cell rate) and improve fairness. In this paper, we propose a new scheduling algorithm for the GFR service. Proposed algorithm provides priority to VC (virtual circuit)s and high Priority given to a VC which has fewer untagged cells in buffer. High priority VCs are serviced before low priority VCs. Proposed algorithm can guarantee MCR and improve fair sharing of the remaining bandwidth between GFR VCs. From computer simulation results, we demonstrate the proposed scheduling algorithm provide much better performance in TCP goodput and fairness than previous schemes.