Plant invasion has been widely recognized as an agent of global change that has the potential to have severe impacts under climate change. The challenges posed by invasive alien plant species (IAPS) on biodiversity and ecosystem stability is growing and not adequately studied, especially in developing countries. Defining climate suitability for multiple invasive plants establishment is important for early and strategic interventions to control and manage plant invasions. We modeled priority IAPS in Sri Lanka to identify the areas of greatest climatic suitability for their establishment and observed how these areas could be altered under projected climate change. We used Maximum Entropy method to model 14 nationally significant IAPS under representative concentration pathways 4.5 and 8.5 for 2050 and 2070. The combined climate suitability map produced by summing up climatic suitability of 14 IAPS was further classified into five classes in ArcMap as very high, high, moderate, low, and very low. South and west parts of Sri Lanka are projected to have potentially higher climatic suitability for a larger number of IAPS. We observed suitable area changes (gains and losses) in all five classes of which two were significant enough to make an overall negative impact i.e., (i) contraction of the very low class and (ii) expansion of the moderate class. Both these changes trigger the potential risk from IAPS in Sri Lanka in the future.