This study evaluates General Circulation Models (GCMs) participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) for their ability in simulating historical means and extremes of daily precipitation (P), and daily maximum (Tmax), and minimum temperature (Tmin). Models are evaluated against hybrid observations at 2255 sub-basins across Alberta, Canada using established statistical metrics for the 1983–2014 period. Three extreme indices including consecutive wet days (CWD), summer days (SD), and warm nights (WN) are defined based on the peak over the threshold approach and characterized by duration and frequency. The tail behaviour of extremes is evaluated using the Generalized Pareto Distribution. Regional evaluations are also conducted for four climate sub-regions across the study area. For both mean annual precipitation and mean annual daily temperature, most GCMs more accurately reproduce the observations in northern Alberta and follow a gradient toward the south having the poorest representation in the western mountainous area. Model simulations show statistically better performance in reproducing mean annual daily Tmax than Tmin, and in reproducing annual mean duration compared to the frequency of extreme indices across the province. The Kernel density curves of duration and frequency as simulated by GCMs show closer agreement to that of observations in the case of CWD. However, it is slightly (completely) overestimated (underestimated) by GCMs for warm nights (summer days). The tail behaviour of extremes indicates that GCMs may not incorporate some local processes such as the convective parameterization scheme in the simulation of daily precipitation. Model performances in each of the four sub-regions are quite similar to their performances at the provincial scale. Bias-corrected and downscaled GCM simulations using a hybrid approach show that the downscaled GCM simulations better represent the means and extremes of P characteristics compared to Tmax and Tmin. There is no clear indication of an improved tail behaviour of GPD based on downscaled simulations.