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Suffering from the double blow of the new crown pneumonia epidemic and floods, food security issues have once again become a source of concern. Eastern Gansu is an important dry farming area in northwestern China, and agricultural production has been greatly affected by climate change. Based on the climate data of 17 national meteorological stations in eastern Gansu from 1961 to 2020 and the data on population, grain planting area and grain production in each region from 1986 to 2019, using the Thornthwaite Memorial model, this paper analyzed the climate production potential (TSPV), population carrying capacity and population carrying capacity index in eastern Gansu, and then revealed the relationship between population and food in eastern Gansu. The findings and results revealed that: (1) over the past 60 years, the temperature in eastern Gansu has been increasing and precipitation has been decreasing; (2) TSPV has been increasing. Moreoever, the spatial distribution was significantly different, showing a trend of decreasing from the southeast to the northwest. Lintao, Huining, and Jingtai displayed a decreasing trend, while other areas exhibited an increasing trend. Precipitation was the main limiting factor for TSPV; (3) Grain production continued to increase due to changing hydrothermal conditions and improved production efficiency. Cultivated land–population carrying capacity and climate production potential–population carrying capacity (TSPV–population carrying capacity) both exhibited a significant increasing trend (p < 0.01). Cultivated land–population capacity increased from southeast to northwest, and all stations expressed an increasing trend. TSPV–population carrying capacity increased from southeast to northwest, and the whole region displayed an increasing trend. Even in extremely reduced production years, TSPV–population carrying capacity was also greater than cultivated land–population carrying capacity. This revealed that, under ideal conditions, TSPV–population carrying capacity can fully meet the needs of the current population. (4) The population carrying capacity index showed a significant downward trend (p < 0.01). It showed a trend of decreasing from south to north, and whole area underwent a decreasing trend consistently, indicating that the population–food relationship in eastern Gansu tended to be balanced. This result was conducive to correct assessment of the relationship between people and food in the study area, and provided a reference for formulating food policies. [ABSTRACT FROM AUTHOR]