To accurately simulate the present and project the late 21st century climates of Japan, we carried out 20-year integrations with a 5-km-mesh, non-hydrostatic regional climate model (NHRCM) nested within a 20-km-mesh Atmospheric Global Circulation Model (AGCM20). The NHRCM simulated monthly mean snow depths more accurately than AGCM20 which used to drive NHRCM. However, NHRCM underestimated snow depths on the Japan Sea side of northern Japan. Because a sample size was insufficient for correcting bias with a cumulative distribution function mapping (CDFM) method at one site, we applied a regional frequency analysis method to group AMeDAS sites in Hokkaido. We tested two kinds of bias corrections: CDFM and a bias correction (designated PBC) based on equating the histograms of model results and observational data. Both methods greatly reduced the biases of simulated snow depths, but PBC produced a greater reduction in the root mean square error in almost every region. The results of PBC indicated that snow depth will decrease more than 80 cm in western parts of Hokkaido in the future.