This paper proposes two modes of the congestion control scheme to improve its behavior during the start-up period of networks in current TCP over ATM-UBR implementation. The proposed two modes are a single packet loss mode and a multiple packet losses mode. The proposed algorithm is to minimize the number of cell losses in the ATM switch during specially the start-up period. During the start-up period, multiple packet losses often happens because a TCP sender starts with default parameters. It often ends up sending too many packets and too fast, leading to multiple losses is packet burstiness which occurs right after fast recovery ends. We analyze the transition behavior during fast recovery algorithm and estimate the number of new packets sent when multiple packet losses detected. We present a simple simulation model and numerical results to investigate its performance of the proposed algorithms.