Understanding climate change impacts on hydrological regime and assessing future water supplies are essential to effective water resources management and planning, which is particularly true for the Tibetan Plateau (TP), one of the most vulnerable areas to climate change. In this study, future climate change in the TP was projected for 2041–2060 by a high‐resolution regional climate model, RegCM4, under 3 representative concentration pathways (RCPs): 2.6, 4.5, and 8.5. Response of all key hydrological elements, that is, evapotranspiration, surface run‐off, baseflow, and snowmelt, to future climate in 2 typical catchments, the source regions of Yellow and Yangtze rivers, was further investigated by the variable infiltration capacity microscale hydrological model incorporated with a 2‐layer energy balance snow model and a frozen soil/permafrost algorithm at a 0.25°×0.25° spatial scale. The results reveal that (a) spatial patterns of precipitation and temperature from RegCM4 agree fairly well with the data from China Meteorological Forcing Dataset, indicating that RegCM4 well reproduces historical climatic information and thus is reliable to support future projection; (b) precipitation increase by 0–70% and temperature rise by 1–4 °C would occur in the TP under 3 RCPs. A clear south‐eastern–north‐western spatial increasing gradient in precipitation would be seen. Besides, under RCP8.5, the peak increase in temperature would approach to 4 °C in spring and autumn in the east of the TP; (c) evapotranspiration would increase by 10–60% in 2 source regions due to the temperature rise, surface run‐off and baseflow in higher elevation region would experience larger increase dominantly due to the precipitation increase, and streamflow would display general increases by more than 3% and 5% in the source regions of Yellow and Yangtze rivers, respectively; (d) snowmelt contributes 11.1% and 16.2% to total run‐off in the source regions of Yellow and Yangtze rivers, respectively, during the baseline period. In the source region of Yangtze River, snowmelt run‐off would become more important with increase of 17.5% and 18.3%, respectively, under RCP2.6 and RCP4.5 but decrease of 15.0% under RCP8.5.