The first consideration of the currency union is the policy commitment versus discretion when the currency union implementing its monetary policy and members of union implementing their fiscal policy decisions. However, since the different process of implementing policies, our model will generate different solutions, including Nash equilibrium (i.e. Monetary and Fiscal policies work simultaneously)、Monetary leadership equilibrium、Fiscal leadership equilibrium. The primary intention of this article is to apply game methods to figure out the output level as well as the inflation rate in all equilibriums. Furthermore, through moral suasion and policy announce mechanism, the central bank of the currency union could also improve the output level obviously and guide the inflation rate to locate in the target.