Guaranteed Frame Rate(GFR), recently approved by the ATM Forum, expects to become an important service category to efficiently support TCP/IP traffic in ATM networks. The GFR service not only guarantees a minimum service rate at the frame level, but also supports a fair share of available bandwidth. We proposed new scheduling scheme for the GFR service. Proposed scheme provides priority to VCs and high priority to a VC which have more untagged cells in buffer. High priority VCs have much more serviced than low priority. Proposed scheme can provide MCR(minimum cell rate) guarantee and fair sharing to GFR VCs. Computer simulation results show that proposed scheduling scheme provide a much better performance in TCP goodput and fairness than previous scheme.