Under global climate warming, the global water cycle is further accelerating, the risk of drought is increasing, and the instability and sustainability of agricultural production are seriously threatened. Northeast China, as the “granary” of China, located in the mid-high latitudes of the Northern Hemisphere, is one of the regions strongly influenced by droughts. Thus, studying the spatial and temporal distribution of drought is helpful for the development of methods for forecasting potential drought hazards in Northeast China. This study used observed data from 86 meteorological stations in Northeast China from 1961 to 2020 to calculate the standardized precipitation evapotranspiration index (SPEI) at different time scales for the past 60 years and analyzed the spatial and temporal characteristics of drought in Northeast China based on the run theory and the Mann-Kendall test. The SPEI at the annual scale showed decreasing trends with no significant mutation point. Seasonally, there was a decreasing trend of the SPEI in summer and autumn and an increasing trend in spring and winter, which indicates that drought in Northeast China has decreased in winter and spring. The annual drought frequency ranged from 25.5% to 37.6%, and the spatial characteristics of the frequency of moderate drought, severe drought, and extreme drought, respectively, showed the following distribution patterns from the western region to the central region and then to the eastern region of Northeast China: “high-low-high”, “low-high-low”, and “gradually decreasing”.