This study analyzed the peak drought severity and drought duration of the Cheongmicheon watershed from 1985 to 2015 to assess the lag time of peak drought severity between several drought indices. Standardized Precipitation Index (SPI) based on precipitation and Standardized Precipitation Evapotranspiration Index (SPEI) based on precipitation and evapotranspiration were applied as meteorological drought indices. Streamflow Drought Index (SDI) based on runoff data was applied as hydrological drought index. In case of SDI, we used Soil and Water Assessment Tool (SWAT) model for simulation of daily runoff data. As a result, the time of peak drought severity of SDI occurred after the occurrence of SPI and SPEI. The lag time for the peak drought severity, on average, between SDI and SPI was 0.59 months while SDI and SPEI was 0.79 months. As compared with SDI, the maximum delay was 2 months for both SPI and SPEI. This study results also shows that even though the rainfall events were able to cope with meteorological droughts, they were not always available to solve the hydrological droughts in the same time.