Based on ensemble calculations with the CMIP6 (Coupled Model Intercomparison Project, phase 6) climate models and using Bayesian averaging, an analysis was conducted on the changes in the 21st century runoff of several Russian rivers – the Volga, Ob, Yenisei, Lena, Amur, and Selenga. Bayesian weights considered the quality of models’ reproduction of runoff (long-term average runoff, linear runoff trend over the time interval with available runoff observations, interannual and interdecadal variability). The quality of runoff characteristics reproduction by individual models in the CMIP6 ensemble varies most significantly for the long-term average runoff, runoff trend, and, to a lesser extent, for interannual variability. In the 21st century, the ensemble average runoff increases for most of the analyzed rivers, except for the Volga. This increase is more pronounced under scenarios with larger anthropogenic impacts. It is especially significant for the SSP5-8.5 scenario (Shared Socioeconomic Pathways, 5-8.5), under which the runoff increase trend from 2015 to 2100 relative to its current long-term average is (10 ± 4)% for the Ob, (16 ± 3)% for the Yenisei, (39 ± 7)% for the Lena, (36 ± 7)% for the Amur, and (18 ± 6)% for the Selenga. The primary reason for the change in ensemble average runoff in the 21st century in models under all SSP scenarios is the change in precipitation. Accounting for differences in model quality in reproducing river runoff on average for 2015–2100 reduces inter-model deviations relative to the corresponding values with uniform weighting of model results by 6–26%, depending on the SSP scenario and river basin.