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Under the influence of climate change, the hydrological processes of glaciers have undergone significant changes, a fact which is seriously affecting agricultural production in the downstream region of the Tianshan Mountains, China. In order to explore the intrinsic relationship between climate change and hydrological elements, we proposed an “evaluation-driving-prediction” system to study it. First, we constructed a glacier-enhanced soil and water assessment tool model (GE-SWAT) and used a two-stage calibration method to optimize the model parameters. Next, a scenario analysis was used to evaluate the driving factors of historical runoff changes. Finally, we projected future runoff changes using bias-corrected regional climate model (RCM) outputs. The results of the case study on the Jinghe River Basin in the Tianshan Mountains show that from 1963 to 2016, total runoff increased by 13.3%, 17.7% of which was due to increasing precipitation and 1.8% of which was negated by rising temperatures. The glacier runoff increased by 14.5%, mainly due to the rising temperatures. A 3.4% reduction in snowmelt was caused by a lower snowfall/precipitation ratio, which significantly reduced the snowfall from June to August. The RCM projection indicated that the warming and humidification phenomenon in the study area will continue at least through to the mid-21st century. A consistent increase in glacier runoff and total runoff is projected, but the contribution rate of the glacier runoff will have little to no change under the RCP4.5 and RCP8.5 emission scenarios. Our research demonstrates the simulation performance of the GE-SWAT model in a basin with moderate glacier cover. This method is shown to be efficient in quantifying the impact of climate change on glacier hydrological processes and predicting future streamflow changes, providing a good research reference for similar regions.