Predictive studies play a crucial role in the study of biological invasions of terrestrial plants under possible climate change scenarios. Invasive species are recognized for their ability to modify soil microbial communities and influence ecosystem dynamics. Here, we focused on six species of allelopathic flowering plants—Ailanthus altissima, Casuarina equisetifolia, Centaurea stoebe ssp. micranthos, Dioscorea bulbifera, Lantana camara, and Schinus terebinthifolia—that are invasive in North America and examined their potential to spread further during projected climate change. We used Species Distribution Models (SDMs) to predict future suitable areas for these species in North America under several proposed future climate models. ENMEval and Maxent were used to develop SDMs, estimate current distributions, and predict future areas of suitable climate for each species. Areas with the greatest predicted suitable climate in the future include the northeastern and the coastal northwestern regions of North America. Range size estimations demonstrate the possibility of extreme range loss for these invasives in the southeastern United States, while new areas may become suitable in the northeastern United States and southeastern Canada. These findings show an overall northward shift of suitable climate during the next few decades, given projected changes in temperature and precipitation. Our results can be utilized to analyze potential shifts in the distribution of these invasive species and may aid in the development of conservation and management plans to target and control dissemination in areas at higher risk for potential future invasion by these allelopathic species.