TCP Reno congestion control carries two issues. First, its performance is poor in high-speed networks. To solve this TCP Reno drawback, HighSpeed TCP and Scalable TCP were proposed. However, the fairness between these proposed TCP and TCP Reno is not considered, when both connections coexist. Second, TCP Reno connections share bandwidth unfairly, when TCP flows with different RTTs use the same link. Many approaches have been proposed to solve this issue. However, no single method has been proposed to solve both issues. In this paper, we propose Square Root Fair TCP (SRF TCP). SRF TCP congestion control (1) sends packets efficiently in high-speed networks, (2) is TCP-friendly with TCP Reno and (3) shares fair bandwidth between flows with different RTTs. We evaluate the capabilities of SRF TCP through computer simulations and compare it with TCP Reno, HighSpeed TCP and Scalable TCP.