Assessments of climate change impacts on streamflow and sediment processes are essential for developing science‐based sustainable watershed management plans. We assessed climate change impacts on streamflow and sediment load in the upstream of the Mekong River Basin, as a case study. Future climate scenarios including an ensemble‐mean climate scenario (EnM scenario) were generated based on 20 GCMs in CMIP5, using a stochastic weather generator (LARS‐WG) coupled with a distribution‐free shuffle procedure. The SWAT model was applied to simulate changes in streamflow and sediment load for the future period 2071–2100 under RCP8.5 with respect to the baseline period 1971–2000. Results show that mean monthly maximum and minimum temperature were projected to increase by all the 20 GCMs, with an ensemble‐mean increase of 4.6–5.7°C and 4.2–5.8°C across the 12 months, respectively. An increase in mean annual precipitation (3.4–55.8%) and streamflow (1.0–72.7%) was also projected by all GCMs. However, projected changes in sediment load were not consistent. One half of the GCMs projected an increase (5.2–53.2%) in annual sediment load while the other half projected a decrease (5.1%–43.2%). In each month, at least three‐quarters of the GCMs projected an increase in monthly streamflow. For monthly sediment load, an increase in May to July was projected by over half of the GCMs, while a decrease was projected by a majority of the GCMs for other months. Our results indicate large uncertainties in streamflow and sediment projections under climate change, demonstrating the need to use multi‐model ensembles in climate change impact studies. Moreover, it was found that the streamflow and sediment loads simulated using the EnM scenario were often close to the ensemble means simulated using the 20 GCMs, which implies that the single EnM scenario has the potential of effectively and efficiently estimating the ensemble means of projections in a multi‐model ensemble. Future temperature, precipitation and streamflow are projected to increase but uncertainties are large. Projected changes in sediment load are not consistent and more uncertain than streamflow. A single ensemble‐mean climate scenario generated using a stochastic approach has the potential of effectively estimating ensemble means of the simulated streamflow and sediment load in a multi‐GCM ensemble.