Potato is the most important non-grain crop in the world. Therefore, understanding the potential impacts of climate change on potato production is critical for future global food security. The SUBSTOR-Potato model was recently evaluated across a wide range of growing conditions, and improvements were made to better simulate atmospheric CO2 and high temperature responses. Comparisons of the improved model with field experiments, including elevated atmospheric CO2 concentrations and high temperature environments, showed a RRMSE of 26% for tuber dry matter. When using the improved model across 0.5 × 0.5° grid cells over all potato-growing regions in the world, the simulated aggregated country tuber dry yields reproduced nationally-reported potato yields with a RRMSE of 56%. Applying future climate change scenarios to current potato cropping systems indicated small global tuber yield reductions by 2055 (−2% to −6%), but larger declines by 2085 (−2% to −26%), depending on the Representative Concentration Pathway (RCP). The largest negative impacts on global tuber yields were projected for RCP 8.5 toward the end of the century. The simulated impacts varied depending on the region, with high tuber reductions in the high latitudes (e.g., Eastern Europe and northern America) and the lowlands of Africa, but less so in the mid-latitudes and tropical highland. Uncertainty due to different climate models was similar to seasonal variability by mid-century, but became larger than year-to-year variability by the end of the century for RCP 8.5.