This chapter focuses on the function of international currencies as foreign exchange vehicles, which has a character of the network externality. On January 1999, the euro was introduced in Europe where the functions of the euro are limed as a currency. After January 2002, the euro had perfect functions, while the competition between the euro and the U.S. dollar was keen as the dominant international currency. We present the currency competition model with a decreasing transaction cost that reflects the character of the network externality, to investigate the competition between the euro and the dollar. We suggest the impact of introduction of the euro is the determinant for competition winner between the euro and the dollar.