The rainfall-runoff characteristics in Jeju Island significantly differ from those in inland, due to highly permeable geologic features driven by volcanic island. Streams are usually sustained in the dry conditions and thereby the rainfall-runoff characteristics changes in terms of initiating stream discharge and its types, depending highly on the antecedent precipitation. Among various the rainfall-runoff characteristics, lag time mainly used for flood warning system in river and direct runoff ratio for determining water budget to estimate groundwater recharge quantity are practically crucial. They are expected to vary accordingly with the given antecedent precipitation. This study assessed the lag time in the measured hydrograph and direct runoff ratio, which are especially in the upstream watershed having the outlet as $2^{nd}$ Dongsan bridge of Han stream, Jeju, based upon several typhoon events such as Khanun, Bolaven, Tembin, Sanba as well as a specific heavy rainfall event in August 23, 2012. As results, considering that the lag time changed a bit over the rainfall events, the averaged lag time without antecedent precipitation was around 1.5 hour, but it became increased with antecedent precipitation. Though the direct run-off ratio showed similar percentages (i.e., 23%)without antecedent precipitation, it was substantially increased up to around 45% when antecedent precipitation existed. In addition, the direct run-off ration without antecedent precipitation was also very high (43.8%), especially when there was extremely heavy rainfall event in the more than five hundreds return period such as typhoon Sanba.