It is well known that TCP does not fully utilize the available bandwidth in fast long-distance networks. This paper proposes S-shaped TCP (SS-TCP). The window growth function of SS-TCP is, in the steady state condition, 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. This paper also proposes SS-TCPW, an enhanced version of SS-TCP. It makes an end-to-end estimation of the available bandwidth as TCP Westwood+. Based on the estimation, SS-TCPW determines the boundary of region III, and decreases its window size. We evaluate the performance of SS-TCP and SS-TCPW in terms of the metrics that are important for high speed transport protocols; buffer requirement, TCP friendliness, RTT fairness and convergence time. The results showed that SS-TCP has much better performance than HighSpeed TCP (HS-TCP) in terms of buffer requirement and RTT fairness. SS-TCPW has better performance than HS-TCP and SS-TCP in all metrics. The results also clarified that SS-TCP and SS-TCPW have much better TCP friendliness than FAST-TCP.