Invasive species threaten biodiversity; hence, predicting where they may establish is vital for conservation. Our aim is to provide a robust predictive model for an invasive species suitable for managers acting at both global and regional scales. Specifically, we investigate one of the world's worst invasive species [the red-eared slider turtle (RES) Trachemys scripta elegans] and one of the world's biodiversity hotspots (New Zealand) as our representative systems. We used climate data and location records to define a bioclimatic envelope for the species. Multimodel inference was used to predict areas suitable for RES establishment, weighting in favour of models with low false-negative and high true-positive rates in predictive cross-validation tests. Our performance criterion was the partial area under the curve of a receiver operating characteristic plot where sensitivity exceeded 0.95. We generated both conservative (best-case scenario) and liberal (worst-case scenario) predictions, based on different levels of information about breeding potential. All predictions were expressed on a standard scale of suitability relative to existing known distribution. Globally, the best climate matches for RES outside of their native range in North America include south-east Asia, and parts of Europe, areas where RES have already established. The best available site in New Zealand is considered climatically more suitable than 16% of global sites where RES have bred successfully. While RES can survive in several areas throughout New Zealand, the potential to establish a self-sustaining (i.e. breeding) population appears restricted to the upper areas of the north island where the mean daily temperatures in the hottest month exceed 18 °C. The methods developed here were designed to reduce false-negative predictions as that represents a precautionary approach for species that pose a biosecurity risk. They could readily be adapted, however, to reduce false-positives when predicting areas suitable for translocation of rare and endangered species.