Climate change and biological invasions are major causes of biodiversity loss and may also have synergistic effects, such as range shifts of invaders due to changing climate. Bioclimatic models provide an important tool to assess how the threat of invasive species may change with altered temperature and precipitation regimes. In this study, potential distributions of three recently naturalised plant species in New Zealand are modelled (Archontophoenix cunninghamiana, Psidium guajava and Schefflera actinophylla), using four different general circulation models (CCCMA-CGCM3, CSIRO-Mk3.0, GFDL-CM2.0 and UKMO-HADCM3) with two emission scenarios (A2 and B1) each. Based on a maximum entropy approach, models were trained on global data using a small set of uncorrelated predictors. The models were projected to the country of interest, using climate models that had been statistically downscaled to New Zealand, in order to obtain high resolution predictions. This study provides evidence of the potential range expansion of these species, with potentially suitable habitat increasing by as much as 169 % (A. cunninghamiana; with up to 115,805 km2 of suitable habitat), 133 % (P. guajava; 164,450 km2) and 208 % (S. actinophylla; 31,257 km2) by the end of the century compared to the currently suitable habitat. The results show that while predictions vary depending on the chosen climate scenario, there is remarkable consistency amongst most climate models within the same emission scenario, with overlaps in areas of predicted presence ranging between 81 % and 99.5 % (excluding CSIRO-Mk3.0). By having a better understanding of how climate change will affect distribution of invasive plants, appropriate management measures can be taken.