We used two common correlative species-distribution models to predict suitable habitat of invasive red lionfish Pterois volitans (Linnaeus, 1758) in the western Atlantic and eastern Pacific Oceans. The Generalized Linear Model (GLM) and the Maximum Entropy (Maxent) model were applied using the Software for Assisted Habitat Modeling. We compared models developed using native occurrences, using non-native occurrences, and using both native and non-native occurrences. Models were trained using occurrence data collected before 2010 and evaluated with occurrence data collected from the invaded range during or after 2010. We considered a total of 22 marine environmental variables. Models built with non-native only or both native and non-native occurrence data outperformed those that used only native occurrences. Evaluation metrics based on the independent test data were highest for models that used both native and non-native occurrences. Bathymetry was the strongest environmental predictor for all models and showed increasing suitability as ocean floor depth decreased, with salinity ranking the second strongest predictor for models that used native and both native and non-native occurrences, indicating low habitat suitability for salinities <30. Our model results also suggest that red lionfish could continue to invade southern latitudes in the western Atlantic Ocean and may establish localized populations in the eastern Pacific Ocean. We reiterate the importance in the choice of the training data source (native, non-native, or native/non-native) used to develop correlative species distribution models for invasive species.