Quantifying the uncertainty sources in assessment of climate change impacts on hydrological processes is helpful for local water management decision-making. This paper investigated the impact of the general circulation model (GCM) structural uncertainty on hydrological processes in the Kaidu River Basin. Outputs of 21 GCMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5) under two representative concentration pathway (RCP) scenarios (i.e., RCP4.5 and RCP8.5), representing future climate change under uncertainty, were first bias-corrected using four precipitation and three temperature methods and then used to force a well-calibrated hydrological model (the Soil and Water Assessment Tool, SWAT) in the study area. Results show that the precipitation will increase by 3.1%–18% and 7.0%–22.5%, the temperature will increase by 2.0 °C–3.3 °C and 4.2 °C–5.5 °C and the streamflow will change by −26% to 3.4% and −38% to −7% under RCP4.5 and RCP8.5, respectively. Timing of snowmelt will shift forward by approximately 1–2 months for both scenarios. Compared to RCPs and bias correction methods, GCM structural uncertainty contributes most to streamflow uncertainty based on the standard deviation method (55.3%) while it is dominant based on the analysis of variance approach (94.1%).