Since the European Union (EU) decided to develop the European Security and Defense Policy (ESDP) in 1999, its achievement is remarkable. The establishment of political and military units, the agreement on military capabilities, all these express the intention of the EU that it actually want to take more responsibility for its security and defense policy. On the other side, the disputes between member states and across the Atlantic deeply affect the development of ESDP. In October 2004, the European Brussels summit accepted the European Constitution. The Constitution may not resolve the disputes which have existed since the end of World War Ⅱ, but it provides at least one goal for EU to follow, which is not aim to be a military power.