Ocean warming associated with global climate change renders marine ecosystems susceptible to biological invasions. Here, we used species distribution models to project habitat suitability for eight invasive ascidians under present-day and future climate scenarios. Distance to shore and maximum sea surface temperature were identified as the most important variables affecting species distributions. Results showed that eight ascidians might respond differently to future climate change. Alarmingly, currently colonized areas are much smaller than predicted, suggesting ascidians may expand their invasive ranges. Areas such as Americas, Europe and Western Pacific have high risks of receiving new invasions. In contrast, African coasts, excluding the Mediterranean side, are not prone to new invasions, likely due to the high sea surface temperature there. Our results highlight the importance of climate change impacts on future invasions and the need for accurate modelling of invasion risks, which can be used as guides to develop management strategies.