Climate change, comprising an increase in carbon dioxide levels coupled with elevated temperature, may favor invasive plants, as they possess traits that will facilitate adaptation to a new climate. In particular, alien plants of subtropical origin introduced to a colder region are expected to increase the number and size of their populations and spread farther with climate change. Seedlings of three such woody alien species in New Zealand (Archontophoenix cunninghamiana, Psidium guajava, and Schefflera actinophylla) were grown in environmental chambers under the combination of two temperature (23.7 and 26 C [74.7 and 78.8 F]) and two CO2 (450 and 900 ppmv) regimes, simulating current conditions and conditions projected for the end of the century. Total biomass of S. actinophylla was 45% higher and total leaf area 35% larger under doubled CO2 compared to current CO2. Root : shoot ratio was higher under doubled CO2 across all species, and the number of branches was increased for P. guajava. The only significant interactive effect of elevated temperature and doubled CO2 was for relative growth rate of the height of S. actinophylla seedlings. This study provides strong evidence of more vigorous growth of S. actinophylla under future conditions, particularly increased CO2, whereas the other two species appear likely to maintain current growth rates. Better knowledge of the types of future conditions that may benefit such species, together with results of species distribution models and competition and eco-physiology studies will ensure robust weed risk assessments.