The Ganges–Brahmaputra–Meghna river system carries the world's third-largest fresh water discharge and Brahmaputra alone carries about 67% of the total annual flow of Bangladesh. Climate change will be expected to alter the hydrological cycles and the flow regime of these basins. Assessment of the fresh water availability of the Brahmaputra Basin in the future under climate change condition is crucial for both society and the ecosystem. SWAT, a semi-distributed physically based hydrological model, has been applied to investigate hydrological response of the basin. However, it is a challenging task to calibrate and validate models over this ungauged and poor data basin. A model derived by using gridded rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite and temperature data from reanalysis product ERA-Interim provides acceptable calibration and validation. Using the SWAT-CUP with SUFI-2 algorithm, sensitivity analysis of model parameters was examined. A calibrated model was derived using new climate change projection data from the multi-model ensemble CMIP5 Project over the South Asia CORDEX domain. The uncertainty of predicting monsoon flow is less than that of pre-monsoon flow. Most of the regional climate models (RCMs) show an increasing tendency of the discharge of Brahmaputra River at Bahadurabad station during monsoon, when flood usually occurs in Bangladesh.