ATM Forum has defined a guaranteed frame rate (GFR) service to serve Internet traffic efficiently. The GFR service provides virtual connections (VCs) for minimum cell rate (MCR) guarantees and allows them to fairly share the residual bandwidth. And ATM Forum has recommended a frame-based generic cell rate algorithm (F-GCRA) as a frame classifier, which determines whether an Am cell is eligible to use the guaranteed bandwidth in a frame level. An ATM switch accommodates cells in its buffer or drops them in a frame level according to current buffer occupancy. A FIFO shared buffer has so simple structure as to be feasibly implemented in switches, but has not been able to provide an MCR guarantee for each VC without buffer management based on per-VC accounting. In this paper, we enhance the F-GCRA frame classifier to guarantee an MCR of each VC without buffer management based on per-VC accounting. The enhanced frame classifier considers burstness of TCP traffic caused by congestion control algorithm so as to enable each VC to use its reserved bandwidth sufficiently. In addition, it is able to alleviate the unfairness problem in usage of the residual bandwidth. Simulation results show that the enhanced frame classifier satisfies quality of services (QoSs) of the GFR service for the TCP traffic.