In this study, the impact of climate change on the streamflow of the Arjo-Didessa catchment, Upper Blue Nile basin, is evaluated. We used the outputs of four climate models for two representative concentration pathway (RCP) climate scenarios, which are RCP 4.5 and RCP 8.5. Streamflow simulation was done by using the HEC-HMS rainfall-runoff model, which was satisfactorily calibrated and validated for the study area. For the historic period (1971–2000), all climate models significantly underestimated the observed rainfall amount for the rainy season. We therefore bias-corrected the climate data before using them as input for the rainfall-runoff model. The results of the four climate models for the period 2041 to 2070 show that annual rainfall is likely to decrease by 0.36 to 21% under RCP 4.5. The projected increases in minimum and maximum temperature will lead to an increase in annual evapotranspiration by 3 to 7%, which will likely contribute to decreasing the annual flows of Arjo-Didessa by 1 to 3%. Our results show that the impact is season dependent, with an increased streamflow in the main rainy season but a decreased flow in the short rainy season and the dry seasons. The magnitudes of projected changes are more pronounced under RCP 8.5 than under RCP 4.5.