Understanding the fine-scale geographic distribution of a species has applications in biogeography, ecology, evolution and conservation. Species distribution models (SDM) have been widely used to predict geographic and climatic ranges of species. Geoffroy’s cat Leopardus geoffroyi is a small felid of least concern that occupies a wide variety of habitat types in Argentina, Bolivia, Brazil, Chile, Paraguay and Uruguay. We evaluated the fine-scale distribution of Geoffroy’s cat at the sub-continental level, estimated its current extent and area of occurrence and discussed the current and potential ranges developed with SDM. On the basis of species occurrences (n = 1502) and large-scale environmental data, two model types (‘environmental’ and ‘land cover’) were developed using MaxEnt. The estimated extent of occurrence of Geoffroy’s cat was 3 180 664 km2, but the potential area of occurrence predicted by our environmental model was 70% larger due to areas with high suitability (i.e. >0.5) compared to the species’ current range. The most important bioclimatic factors affecting Geoffroy’s cat presence were temperature seasonality, mean temperature of the coldest quarter and annual precipitation. Two recent records obtained outside the known distribution of the species fell within the high-suitability area (i.e. >0.5) predicted by our model. Our SDM suggest that this habitat-generalist felid is probably expanding its distribution range by taking advantage of changes in human land use.