When predicting the potential and future invasive range of a species, there is a growing appreciation that insights about factors limiting distributions can be provided by using multiple modelling approaches and by incorporating information from different parts of a species range. Here we apply this strategy to build on previous CLIMEX models to predict the invasion potential of Aedes albopictus, the Asian tiger mosquito, in mainland Australia. A combination of CLIMEX and MAXENT modelling indicated that the mosquito was expected to become widespread along the eastern seaboard and extend into northern Tasmania, but to remain restricted to the coastal fringe, a pattern which is not expected to shift much under climate change. However, a recent expansion of A. albopictus in North America points to evolutionary changes affecting the distribution of this species; when the North American range is included in models, A. albopictus is predicted to become much more widespread and extend inland and into Western Australia. These patterns highlight the potential impact of evolution on species distributions arising from multiple introductions or in situ evolution. By considering future climate scenarios, we demonstrate that there is likely to be a persistent public health threat associated with invasion by this species.