Increasing air temperature and atmospheric CO2 levels may affect the distribution of invasive species. Whereas there is wide knowledge on the effect of global change on temperate species, responses of tropical invasive species to these two global change drivers are largely unknown. We conducted a greenhouse experiment on Terminalia catappa L. (Combretaceae), an invasive tree species on Brazilian coastal areas, to evaluate the effects of increased air temperature and CO2 concentration on seed germination and seedling growth on the island of Santa Catarina (Florianópolis, Brazil). Seeds of the invasive tree were subjected to two temperature levels (ambient and +1.6 °C) and two CO2 levels (ambient and ~650 ppmv) with a factorial design. Increased temperature enhanced germination rate and shortened germination time of T. catappa seeds. It also increased plant height, number of leaves and above‐ground biomass. By contrast, increased atmospheric CO2 concentration had no significant effects, and the interaction between temperature and CO2 concentration did not affect any of the measured traits. Terminalia catappa adapts to a relatively broad range of environmental conditions, being able to tolerate cooler temperatures in its invasive range. As T. catappa is native to tropical areas, global warming might favour its establishment along the coast of subtropical South America, while increased CO2 levels seem not to have significant effects on seed germination or seedling growth.