Drought is a natural disaster in which the land surface suffers a severe water shortage for a long time. Unlike other natural disasters, determining the beginning and the end of the drought is difficult, so drought can have different meanings and categories according to the application purposes. In this paper, we presented the Potential Water Stress Index (PWSI), a new drought index by combining satellite-based precipitation and potential evapotranspiration data in terms of water supply and consumption of the land surface. In the case study for the Korean Peninsula, we analyzed two types of droughts: (i) a typical drought due to the lack of precipitation and (ii) a sudden drought due to extraordinary heatwaves and excessive evapotranspiration. The proposed PWSI could express both types of droughts well, while Standardized Precipitation Index (SPI) was not appropriate for the sudden drought. Moreover, the PWSI agreed with the pattern of vegetation health with some time lags. Under the rapid increase of climate change, the sudden drought, which has not been introduced well, can be more frequent in the future. Therefore the proposed PWSI can help the expression of agricultural droughts in the context of the relationship between water stress and vegetation health. Real-time or high-resolution data can support more effective management of droughts in monitoring systems.