It is known that TCP throughput can degrade significantly over UBR service in a congested ATM network, and the early packet discard (EPD) technique has been proposed to improve the performance. However, recent studies show that EPD cannot ensure fairness among competing VCs in a congested network, but the degree of fairness can be improved using various forms of fair buffer allocation techniques. Based upon the work by H.Y. Tzeng and K.Y. Siu (1996), we propose an improved scheme that utilizes only a single shared FIFO queue for all VCs and admits simple implementation for high speed ATM networks. Our scheme achieves nearly perfect fairness of throughput among multiple TCP connections, comparable to the expensive per-VC queuing technique. Analytical and simulation results are presented to show the validity of this new scheme and significant improvement in performance as compared with existing fair buffer allocation techniques for TCP over ATM.