The Yalong River basin (YRB), originating from the Tibetan Plateau, is critical for China's western development and electricity transmission. Climate change would affect the streamflow and potentially impact the hydropower in the YRB. In this study, the Automated Statistical Downscaling technique and the hydrological model SWAT were used to reproduce the observed precipitation, temperature and streamflow and predict them in the future. More importantly, the Bayesian Model Averaging (BMA) method was used to appraise the performance of four different Global Climate Models (GCMs) in simulating historical streamflow (1984–1997), and to quantify the uncertainties in future projections (2021–2100) under three Representative Concentration Pathways (RCPs) in the YRB. It was found that (i) the SWAT hydrological model has good applicability in the YRB; (ii) the BMA method can capture the historical streamflow reasonably better than individual GCM projections, providing a scientific reference for the future water resources planning and utilization in the YRB.