In this paper, we propose a new congestion control scheme for high-speed networks. The basic idea of our proposed scheme is to adopt a game theory called, "Minority Game" (MG), to realize a selective reduction of the transmission speed of senders. More concretely, upon detecting any congestion, the scheme starts a game among all senders who are participating in the communication. The losers of the game reduce the transmission speed by a multiplicative factor. MG is a game that has recently attracted considerable attention, and it is known to have a remarkable property so that the number of winners converges to a half the number of players in spite of the selfish behavior of the players to increase its own profit. By using this property of MG, we can realize a fair reduction of the transmission speed, which is more efficient than the previous schemes in which all senders uniformly reduce their transmission speed. The effect of the proposed scheme is evaluated by simulation. The result of simulations indicates that the proposed scheme certainly realizes a selective reduction of the transmission speed. It is sufficiently fair compared to other simple randomized schemes and is sufficiently efficient compared to other conventional schemes.