This study examines the asymmetric volatility from the viewpoint of the information inefficiency in the won/dollar, won/yen, won/euro, yen/dollar, euro/dollar from January 1998 to April 2009. If the asymmetric volatility declines over time, it may be interpreted as the information inefficiency declines. This may confirm the appropriateness of Adaptive Market Hypothesis in the Korean foreign exchange market. From the point of view of the central bank policy, the declination of the asymmetric volatility over time may imply the declination of the impact of the central bank’s action over time. Both of the interpretations may signal the applicability of Adaptive Market Hypothesis in the Korean Foreign Exchange Market. Empirical study on won/dollar, won/yen monthly data shows that volatility clustering exists but volatility asymmetry does not even after the sub-prime crisis, which clearly shows that Adaptive Market Hypothesis is applicable in the Korean Foreign Exchange Market. But, for daily data it is found that the mean equation parameters and volatility asymmetry pattern changes after the sub-prime crisis, which clearly shows that daily foreign exchange rate change reflects the incoming information. Especially the asymmetry parameters have negative signs, which implies that dollar and yen are considered as a base currency from won’s point of view. However this phenomenon may also be interpreted as the information efficiency reflecting the sub prime crisis.