Climate change and globalization are as many factors that promote biological invasions with potentially important negative impact on biodiversity, agriculture or public health. In the case of crop and fruit pest species, the prediction of the risk of establishment and spreading of populations outside there native range therefore represents a major challenge. To address this issue, some population genomics approaches may be viewed as particularly well suited. Indeed, they allow a better understanding of the factors favoring local adaptation of populations by valuing genetic information. For illustrative purpose, we studied the crop pest species Drosophila suzukii, native from Asia, which has rapidly invaded American and European continents in the early 2010s. By combining several public data sets, we estimated allelic frequencies for 3,224,737 SNP genetic markers for 43 population samples (22 sequenced in pool and 21 represented by 162 sequenced individuals) representative of both the native and invaded areas. We then used the recently developed machine learning method called “Gradient Forest” which relies on random forests, to model the association between genetic diversity across populations and 19 bioclimatic variables. The triple aim of this analysis was i) to identify the more influential climatic variables for local adaptation of the populations and likely influencing the invasion dynamic; ii) to evaluate, using genomic information, the degree of “maladaptation” measured by the so-called “genomic offset” of the populations to an environment different from the one they originated from ; iii) to evaluate to which extent “genomic offset” represents a good predictor of the invasiveness of some populations by comparing the obtained values with the known recent invasion dynamic of D. suzukii species. We overall found that “Gradient Forest” approaches are promising to provide insights into biological invasion from genomic data although some limitations need to be investigated further.