It is well known that TCP does not fully utilize the available bandwidth in fast long-distance networks. To solve this scalability problem, this paper proposes S-shaped TCP (SSTCP). The window growth function of SS-TCP is, in the steady state, S-shaped, and it can be divided into three regions. In region I, the window growth rate of SS-TCP is the same as that of standard TCP (STD-TCP). In region II, the window of SS-TCP grows faster than that of STD-TCP. In region III, SS-TCP decreases its window growth rate as the network is becoming congested.