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Satellite-based remote sensing techniques have been widely used to monitor droughts spanning large areas. Various agricultural drought indices have been developed to assess the intensity of agricultural drought and to detect damaged crop areas. However, to better understand the responses of agricultural drought to meteorological drought, agricultural management practices should be taken into consideration. This study aims to evaluate the responses to drought under different forms of agricultural management for the extreme drought that occurred on the Korean Peninsula in 2014 and 2015. The 3-month standardized precipitation index (SPI3) and the 3-month vegetation health index (VHI3) were selected as a meteorological drought index and an agricultural drought index, respectively. VHI3, which comprises the 3-month temperature condition index (TCI3) and the 3-month vegetation condition index (VCI3), differed significantly in the study area during the extreme drought. VCI3 had a different response to the lack of precipitation in South and North Korea because it was affected by irrigation. However, the time series of TCI3 were similar in South and North Korea. These results meant that each drought index has different characteristics and should be utilized with caution. Our results are expected to help comprehend the responses of the agricultural drought index on meteorological drought depending on agricultural management.