After two world wars, the West European Economy goes through serious recession. Through the cold war, the representatives of west European countries, German and France, feel that they must cooperate. Hence, by the bases of economic co-operations, the West Europe starts to integrate their resources and political alliances. From the ¡§Economic Community (EC)¡¨ to ¡§Economic and Monetary Union (EMU)¡¨, most West European countries go through several obstacles, like the Collapse of Bretton Woods System in 1971 and the European Crisis in 1992,¡K¡K, etc. Finally, in 1th, Jan., 1999, 11 countries of European Union establish EMU and expect to take Euro as their single currency formally in 2002. They also establish European Central Bank (ECB) to execute the Euro zone¡¦s single monetary policy. The status of Euro after 1th Jan., 1999 is the purpose of this study. This article tries to use the Exchange Rate decision theories, Purchasing Power Parity (PPP) and Interest Rate parity (IRP), to investigate the relationship between Euro and USD. From several statistical empirical tests, it reveals that the trends of Euro couldn¡¦t correspond with the theoretical wants, ie PPP and IRP can¡¦t catch the trends of Euro. By the outcome of ¡§Sign Test¡¨ and ¡§Wilcoxon Sign-Rank Test¡¨, it can be found obviously that the Euro indeed is undervalued from the establishment to Apr., 2000 if we don¡¦t take the transaction costs into account. As a result of the outcome of empirical finds, the article starts to investigate the reasons why the theoretical values from exchange rate decision theories are not equal with real ones. One is that if the empirical models ignore some important factors which lead to the biases of models¡Fthe other is if Euro is undervalued during this observation periods. From the economic macro-environmental analyses, the article can infer that because of the Kosov Wars, Russian economic reform problems, the increase of short interest rate gap between USD and Euro, the different economic reform paces among member countries of EMU,¡K¡K, etc. result in the main factors of the weak currency - Euro.