Predictive studies are of paramount importance for biological invasions, one of the biggest threats for biodiversity. To help and better prioritize management strategies, species distribution models (SDMs) are often used to predict the potential invasive range of introduced species. Yet, SDMs have been regularly criticized, due to several strong limitations, such as violating the equilibrium assumption during the invasion process. Unfortunately, validation studies–with independent data–are too scarce to assess the predictive accuracy of SDMs in invasion biology. Yet, biological invasions allow to test SDMs usefulness, by retrospectively assessing whether they would have accurately predicted the latest ranges of invasion. Here, we assess the predictive accuracy of SDMs in predicting the expansion of invasive species. We used temporal occurrence data for the Asian hornet Vespa velutina nigrithorax, a species native to China that is invading Europe with a very fast rate. Specifically, we compared occurrence data from the last stage of invasion (independent validation points) to the climate suitability distribution predicted from models calibrated with data from the early stage of invasion. Despite the invasive species not being at equilibrium yet, the predicted climate suitability of validation points was high. SDMs can thus adequately predict the spread of V. v. nigrithorax, which appears to be—at least partially–climatically driven. In the case of V. v. nigrithorax, SDMs predictive accuracy was slightly but significantly better when models were calibrated with invasive data only, excluding native data. Although more validation studies for other invasion cases are needed to generalize our results, our findings are an important step towards validating the use of SDMs in invasion biology.