During range expansions, even low levels of interbreeding can lead to massive introgression of local alleles into an invader's genome. Nonetheless, this pattern is not always observed in human populations. For instance, European Americans in North America are barely introgressed by Amerindian genes in spite of known contact and admixture. With coalescent spatially explicit simulations, we examined the impact of long-distance dispersal (LDD) events on introgression of local alleles into the invading population using a set of different demographic scenarios applicable to a diverse range of natural populations and species. More specifically, we consider two distinct LDD models: one where LDD events originate in the range core and targets only the expansion front and a second one where LDD events can occur from any area to any other. We find that LDD generally prevents introgression, but that LDD events specifically targeting the expansion front are most efficient in suppressing introgression. This is likely due to the fact that LDD allows for the presence of a larger number of invader alleles at the wave front, where effective population size is thus increased and local introgressed alleles are rapidly outnumbered. We postulate that the documented settlement of pioneers directly on the wave front in North America has contributed to low levels of Amerindian admixture observed in European Americans and that this phenomenon may well explain the lack of introgression after a range expansion in natural populations without the need to evoke other mechanisms such as natural selection.