We extend the open economy model of optimal monetary policy to incorporate asymmetric exchange rate pass-through, with a focus on the effect of sticky price on monetary policy transmission and welfare analysis. Under incomplete pass-through inthe home country and full pass-through inthe foreign country, we find that country-specific productivity shocks have complex effects on optimal monetary policies, which also depend on the elasticity of money demand. In a world Nash equilibrium, foreign monetary policy depends on the degree of home exchange rate pass-through. Asymmetry in exchange rate pass-through leads to asymmetric welfare effects. The welfare level of the home country is higher than that of the foreign country in the Nash equilibrium.However, international cooperation can improve world welfare level. 《Annals of Economics & Finance》, 2016, 17