Exploring the response relationship between hydrological and meteorological droughts is of great significance for establishing a sound drought monitoring and forecasting system. Drought characteristics were extracted using a combination of the regional hydrological drought index (SHI) and standardized precipitation index (SPI), then the response relationship and driving factors of hydrological droughts and meteorological droughts in Kashi River Basin were analyzed by nonlinear function model and runs theory. The results indicate that the average annual drought duration and magnitude of hydrological droughts were greater than that of meteorological droughts, and with the increase of SPI and SHI time scale, the identified drought duration and magnitude also increased. The logarithmic function model with three parameters can be used to better characterize the response relationship between hydrological and meteorological droughts. According to this model, when the meteorological drought last no less than 1.10 months and the drought magnitude is no less than 0.83, the hydrological drought will be induced at 3-month scale. When the meteorological drought last no less than 1.60 months and the drought magnitude is no less than 0.91, the hydrological drought will easily occur at 6-month scale.