Simulation of future climate changes, especially temperature and rainfall, is critical for water resource management, disaster mitigation, and agricultural development. Based on the category-wise indicator method, two preferred Global Climate Models (GCMs) for the Ishikari River basin (IRB), the socio-economic center of Hokkaido, Japan, were examined from the newly released Coupled Model Intercomparison Project Phase 6 (CMIP6). Climatic variables (maximum/minimum temperature and precipitation) were projected by the Statistical DownScaling Model (SDSM) under all shared socioeconomic pathway-representative concentration pathway (SSP-RCP) scenarios (SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP4-3.4, SSP4-6.0, SSP5-3.4OS, and SSP5-8.5) in two phases: 2040–2069 (2040s) and 2070–2099 (2070s), with the period of 1985–2014 as the baseline. Predictors of SDSM were derived from CMIP6 GCMs and the reanalysis dataset NOAA-CIRES-DOE 20th Century Reanalysis V3 (20CRv3). Results showed that CMIP6 GCMs had a significant correlation with temperature measurements, but could not represent precipitation features in the IRB. The constructed SDSM could capture the characteristics of temperature and precipitation during the calibration (1985–1999) and validation (2000–2014) phases, respectively. The selected GCMs (MIROC6 and MRI-ESM-2.0) generated higher temperature and less rainfall in the forthcoming phases. The SSP-RCP scenarios had an apparent influence on temperature and precipitation. High-emission scenarios (i.e., SSP5-8.5) would project a higher temperature and lower rainfall than the low-emission scenarios (e.g., SSP1-1.9). Spatial–temporal analysis indicated that the northern part of the IRB is more likely to become warmer with heavier precipitation than the southern part in the future. Higher temperature and lower rainfall were projected throughout the late twenty-first century (2070s) than the mid-century (2040s) in the IRB. The findings of this study could be further used to predict the hydrological cycle and assess the ecosystem's sustainability.