Precisely quantitative assessments of stream flow response to climatic change and permafrost thawing are highly challenging and urgent in cold regions. However, due to the notably harsh environmental conditions, there is little field monitoring data of runoff in permafrost regions, which has limited the development of physically based models in these regions. To identify the impacts of climate change in the runoff process in the Three-River Headwater Region (TRHR) on the Qinghai-Tibet Plateau, two artificial neural network (ANN) models, one with three input variables (previous runoff, air temperature, and precipitation) and another with two input variables (air temperature and precipitation only), were developed to simulate and predict the runoff variation in the TRHR. The results show that the three-input variable ANN model has a superior real-time prediction capability and performs well in the simulation and forecasting of the runoff variation in the TRHR. Under the different scenarios conditions, the forecasting results of ANN model indicated that climate change has a great effect on the runoff processes in the TRHR. The results of this study are of practical significance for water resources management and the evaluation of the impacts of climatic change on the hydrological regime in long-term considerations.