Since arid and semi-arid regions are sensitive and vulnerable to both climate change and human activities, studying the spatiotemporal evolution characteristics of droughts helps understanding disaster mechanism. The Hedong region (HDR) in Gansu Province is a typical arid and semi-arid region, which depends on precipitation to maintain agricultural production. Meteorological and hydrological droughts are detected based on the standardized precipitation index and the standardized runoff index. The results show that: (1) Meteorological droughts in HDR mostly occur from spring to summer in the Longdong area, with a duration of less than three months. (2) Hydrological droughts last longer compared to meteorological droughts and may occur at multi-year scales. (3) The propagation between meteorological and hydrological droughts is varied in different seasons. There is almost no lag time in spring and summer, about one month in autumn and four months in winter. (4) The areas affected by drought disaster most are the Longzhong and Longdong regions. This study provides scientific guidance for drought early-warning and prevention in arid and semi-arid regions.