We propose a novel theory for the evolution of polyandry driven by genetic benefits to females whose offspring interbreed. In species with an ecology characterized by frequent colonization of new habitat patches, consanguineous matings may be common during the early stages of colonization, but genetic diversity may grow as new colonizers arrive. We show that with levels of inbreeding depression similar to those found in predominantly inbreeding populations, a polyandrous female can benefit her descendants since matings among her brood are mainly between half siblings rather than full siblings. We examine the invasion by a polyandrous phenotype using explicit genetic models in which costs of inbreeding are themselves subject to selection. In common with other models of inbreeding, we find that underlying high levels of inbreeding tend to purge deleterious recessive alleles, and hence these are unlikely to maintain sufficient inbreeding depression to favour polyandry. However, if costs of inbreeding are due to overdominance, biologically realistic levels of inbreeding depression result in genetic benefits large enough to favour polyandry provided it is not too costly. The potential significance of polyandry as a mechanism to reduce inbreeding in grandchildren will depend upon the genetic basis of inbreeding depression in natural, inbreeding populations.