Understanding the determinants of the range expansion of invasive alien species is crucial for developing effective prevention and control strategies. Nevertheless, we still lack a global picture of the potential factors influencing the invaded range expansion across taxonomic groups, especially for the world's worst invaders with high ecological and economic impacts. Here, by extensively collecting data on 363 distributional ranges of 19 of world's worst invasive terrestrial vertebrates across 135 invaded administrative jurisdictions, we observed remarkable variations in the range expansion across species and taxonomic groups. After controlling for taxonomic and geographic pseudoreplicates, model averaging analyses based on generalized additive mixed‐effect models showed that species in invaded regions having climates more similar to those of their native ranges tended to undergo a larger range expansion. In addition, as proxies of propagule pressure and human‐assisted transportation, the number of introduction events and the road network density were also important predictors facilitating the range expansion. Further variance partitioning analyses validated the predominant role of climate match in explaining the range expansion. Our study demonstrated that regions with similar climates to their native ranges could still be prioritized to prevent the spread of invasive species under the sustained global change.