This paper proposes a new TCP congestion control supporting loss-fairness, which also contributes to improving RTT fairness. It has been well known that smaller RTT flows grab more bandwidth than larger ones when they compete on the shared link. This is called RTT unfairness and is caused by congestion control mechanism of the current TCP. To solve this problem, many protocols have been proposed. TCP-Libra is one of them, which formulates its window increase rate as a function of RTT and brings the same throughput irrespective of different RTT values. However, we indicate TCP-Libra's formulation holds only when the congestion window is halved upon packet losses similar to TCP-Reno. When we apply different (smarter) window control schemes, the formulation has to be modified accordingly. Therefore, in this paper, we consider a hybrid congestion control supporting RTT fairness which switches two modes according to buffering state at the bottleneck link. In decrement phase upon packet loss, it decreases window size to clear the buffering packets instead of halving the window size. Furthermore, we introduce the concept of loss-fairness for our window increase formulation, which is equivalent to RTTfairness. Experiments are carried out to validate the proposed method by both implementation experiments and simulations, and much better performances are achieved against conventional methods.