The Brahmaputra River Basin (BRB) is one of the major fresh water sources in South Asia. The current research attempts to assess impacts of climate change on streamflow of BRB using a physically based semidistributed hydrological model, namely, soil and water assessment tool (SWAT). SWAT was calibrated and validated for the climate normal period (1981–2010) at the Bahadurabad station in Bangladesh, and good agreement between observed and simulated streamflow was found. The model was then applied to simulate 24 synthetic climate change scenarios (combination of perturbed precipitation and temperature) to investigate the basin’s sensitivity, in terms of streamflow, under the potential impact of climate change. It was found that the basin’s projected streamflow responded almost linearly with projected temperature and precipitation. Mean annual streamflow changes of the BRB due to 1°C change in temperature (keeping the 1981–2010 baseline precipitation unchanged) was about 1.35%, whereas about 1.37% changes in mean annual streamflow were projected for 1% change in precipitation (keeping the baseline temperature unchanged). The results obtained using perturbed scenarios were used to develop a multivariable linear regression model representing future streamflow of BRB under the projected changes in temperature and precipitation..