Bottlenecks in population size reduce genetic diversity and increase inbreeding, which can lead to inbreeding depression. It is thus puzzling how introduced species, which typically pass through bottlenecks, become such successful invaders. However, under certain theoretical conditions, bottlenecks of intermediate size can actually purge the alleles that cause inbreeding depression. Although this process has been confirmed in model laboratory systems, it has yet to be observed in natural invasive populations. We evaluate whether such purging could facilitate biological invasions by using the world-wide invasion of the ladybird (or ladybug) Harmonia axyridis. We first show that invasive populations endured a bottleneck of intermediate intensity. We then demonstrate that replicate introduced populations experience almost none of the inbreeding depression suffered by native populations. Thus, rather than posing a barrier to invasion as often assumed, bottlenecks, by purging deleterious alleles, can enable the evolution of invaders that maintain high fitness even when inbred.