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Under global climate changes, the temperature and precipitation on the Tibetan Plateau changed significantly, causing accelerated melting of glaciers and snow and changes in runoff. The response of runoff and its components to climate change is important for water resource management and ecology conservation in the region. Therefore, the Spatial Processes in Hydrology model, a distributed cold‐zone hydrological model that contains a glacial ablation module, was used to simulate runoff in the Yangtze River source located in the middle of the Tibetan Plateau during 2000–2050, and the Nash‐Sutcliffe efficiency coefficient, relative error and coefficient of determination (R2) for the calibration period and validation period revealed that the model performed well in most years. The results showed that rainfall runoff contributed the most to the total runoff (61%), followed by baseflow (23%), snowmelt runoff (12%) and glacier runoff (4%) in the Yangtze River source during 2000–2020. The runoff amounts of the three source rivers, Dangqu River, Tuotuo River and Chumar River, accounted for approximately 53% of the total runoff in the Yangtze River source basin, with rainfall runoff (52%) contributing the most and glacier runoff (6%) contributing the least. Compared to the contributions of glacial runoff in the Dangqu River (9%) and Tuotuo River (7%), the proportion of glacial runoff in the Chumar River is small (1%). Under the CMIP6 climate model, the mean runoff depth is predicted to increase by approximately 13.5 mm from 2020 to 2050 compared with that from 2000 to 2020. [ABSTRACT FROM AUTHOR]