Climate projections for continental Europe indicate drier summers, increased annual precipitation, and less snowy winters, which are expected to cause shifts in species' distributions. Yet, most regions/countries currently lack comprehensive climate‐driven biodiversity projections across taxonomic groups, challenging effective conservation efforts. To address this gap, our study evaluated the potential effects of climate change on the biodiversity of an alpine country of Europe, Switzerland. We used a state‐of‐the art species distribution modeling approach and species occurrence data that covered the climatic conditions encountered across the full species' ranges to help limiting niche truncation. We quantified the relationship between baseline climate and the spatial distribution of 7291 species from 12 main taxonomic groups and projected future climate suitability for three 30‐year periods and two greenhouse gas concentration scenarios (RCP4.5 and 8.5). Our results indicated important effects of projected climate changes on species' climate suitability, with responses varying by the taxonomic and conservation status group. The percentage of species facing major changes in climate suitability was higher under RCP8.5 (68%) compared to RCP4.5 (66%). By the end of the century, decreases in climate suitability were projected for 3000 species under RCP8.5 and 1758 species under RCP4.5. The most affected groups under RCP8.5 were molluscs, algae, and amphibians, while it was molluscs, birds, and vascular plants under RCP4.5. Spatially, by 2070–2099, we projected an overall decrease in climate suitability for 39% of the cells in the study area under RCP8.5 and 10% under RCP4.5, while projecting an increase for 50% of the cells under RCP8.5 and 73% under RCP4.5. The most consistent geographical shifts were upward, southward, and eastward. We found that the coverage of high climate suitability cells by protected areas was expected to increase. Our models and maps provide guidance for spatial conservation planning by pointing out future climate‐suitable areas for biodiversity.