This contribution aimed to predict the invasive Barbary ground squirrel (Atlantoxerus getulus) potentiality for invading the Canary Islands and western Mediterranean region, by determining firstly the climatic suitable areas in its native range and secondly, using presence data in the invaded range. Nineteen environmental variables submitted to a Principal Components Analysis selected those variables with higher factor loadings, which represent the main environmental conditions of the Northern African region (temperature in the coldest quarter, seasonal temperature, precipitation in the coldest quarter, temperature in the wettest quarter). After selecting hundred times more pseudo-absence points than presence observations (n = 6600 at a 0.083° resolution), Generalized Additive Models and Single-hidden-layer Neural Networks fitted in R were used to calibrate the model. Model results were extrapolated for the Canary Islands and the western Mediterranean region. In order to select between the two techniques, we calculated three accuracy measures (specificity, sensitivity and AUC) after using a Jack-knifing procedure and models were repeated ten times. The GAM model was less accurate than the NN model. Suitable areas did not have mean temperatures in the coldest quarter lower than -5°C and precipitation in the coldest quarter higher than 300 mm, respectively. We predicted favorable climatic areas across almost all the Maghreb, the European western Mediterranean region and in all the Canary Islands. Nevertheless, the seven islands differed significantly in the mean favorability scores, with El Hierro, Lanzarote and Gran Canaria being the most suitable. Same methodological analysis was applied to predict A. getulus distribution in other Canarian islands based on presence data from the invaded Fuerteventura. In this case, only Lanzarote and Gran Canaria appeared to be climatically suitable for the species. Our predictive model is an applicable tool to establish the invasive potential of A. getulus and to prioritize management strategies, within and outside the Canarian archipelago, to impede the expansion of this invasive squirrel out of Fuerteventura Island.