In many regions, large proportions of the naturalized and invasive non-native floras were originally introduced deliberately by humans. Pest risk assessments are now used in many jurisdictions to regulate the importation of species and usually include an estimation of the potential distribution in the import area. Two species of Asian grass (Miscanthus sacchariflorus and M. sinensis) that were originally introduced to North America as ornamental plants have since escaped cultivation. These species and their hybrid offspring are now receiving attention for large-scale production as biofuel crops in North America and elsewhere. We evaluated their potential global climate suitability for cultivation and potential invasion using the niche model CLIMEX and evaluated the models' sensitivity to the parameter values. We then compared the sensitivity of projections of future climatically suitable area under two climate models and two emissions scenarios. The models indicate that the species have been introduced to most of the potential global climatically suitable areas in the northern but not the southern hemisphere. The more narrowly distributed species (M. sacchariflorus) is more sensitive to changes in model parameters, which could have implications for modelling species of conservation concern. Climate projections indicate likely contractions in potential range in the south, but expansions in the north, particularly in introduced areas where biomass production trials are under way. Climate sensitivity analysis shows that projections differ more between the selected climate change models than between the selected emissions scenarios. Local-scale assessments are required to overlay suitable habitat with climate projections to estimate areas of cultivation potential and invasion risk.