Rivers are the main source of fresh water in mountainous and downstream areas. It is crucial to investigate the possible threats of climate change and understand their impact on river watersheds. In this research, climate change’s impact on the mountainous watershed of the Jajrood River, upstream of Latyan Dam in Iran, was assessed by using a multivariate recursive quantile-matching nesting bias correction (MRQNBC) and the soil and water assessment tool (SWAT). Also, this study considered ten global circulation models (GCMs) from the coupled model intercomparison project phase VI (CMIP6). With a higher correlation coefficient, the MIROC6 model was selected among other models. For the future period of 2031–2060, the large-scale outputs of the MIROC6 model, corresponding to the observational data were extracted under four common socioeconomic path scenarios (SSPs 1–2.6, 2–4.5, 3–7.0, 5–8.5). The bias was corrected and downscaled by the MRQNBC method. The downscale outputs were given to the hydrological model to predict future flow. The results show that, in the period 2031–2060, the flow will be increased significantly compared to the base period (2005–2019). This increase can be seen in all scenarios. In general, changes in future flow are caused by an increase in precipitation intensity, as a result of an increase in temperature. The findings indicate that, although the results show an increase in the risk of flooding, considering the combined effects of three components, i.e., increased precipitation concentration, temperature, and reduced precipitation, climate change is intensifying the problem of water scarcity.