This paper investigates how differently won/dollar real exchange rate impacts the export volume to the world and to the US. for the four Korean export industries. Using monthly data of Korean exports to the world and to the US. from 2000:01 to 2014:06, and a bivariate GARCH estimator with corrections for leptokurtic errors, the paper shows that won/dollar real exchange rate volatility has positive and significant impact on Korean heavyweight industry's export to the world, while won/dollar real exchange rate volatility has negative and insignificant impact on Korean heavyweight industry's export to the US.. The impact of won/dollar on the other three industries (food, material, lightweight) is not significant for both markets. This finding implies that whether the claim that exchange rate volatility impacts trade volume negatively or not depends on the destination of the export, where the relative competitiveness of the Korean export industry is revealed. Won/dollar real exchange rate volatility has positive and significant impact on the volatility of heavyweight industry's export to the world, which may imply possible positive and accelerating effect to the export to the world with favorable won/dollar movement, reflecting heavyweight industry's strong competitiveness in the world market. However the positive and significant volatility impact of won/dollar real exchange rate volatility on heavyweight and lightweight industries' export to the US. may imply possible negative and insignificant effect with favorable won/dollar movement, reflecting weak competiveness of the two Korean industries in the U.S. market.