The giant hogweed (Heracleum mantegazzianum) has successfully invaded 19 European countries as well as parts of North America. It has become a problematic species due to its ability to displace native flora and to cause public health hazards. Applying population genetics to species invasion can help reconstruct invasion history and may promote more efficient management practice. We thus analysed levels of genetic variation and population genetic structure of H. mantegazzianum in an invaded area of the western Swiss Alps as well as in its native range (the Caucasus), using eight nuclear microsatellite loci together with plastid DNA markers and sequences. On both nuclear and plastid genomes, native populations exhibited significantly higher levels of genetic diversity compared to invasive populations, confirming an important founder event during the invasion process. Invasive populations were also significantly more differentiated than native populations. Bayesian clustering analysis identified five clusters in the native range that corresponded to geographically and ecologically separated groups. In the invaded range, 10 clusters occurred. Unlike native populations, invasive clusters were characterized by a mosaic pattern in the landscape, possibly caused by anthropogenic dispersal of the species via roads and direct collection for ornamental purposes. Lastly, our analyses revealed four main divergent groups in the western Swiss Alps, likely as a consequence of multiple independent establishments of H. mantegazzianum.