Many animals have evolved strategies to reduce risks of inbreeding and its deleterious effects on the progeny. In social arthropods, such as the eusocial ants and bees, inbreeding avoidance is typically achieved by the dispersal of breeders from their native colony. However studies in presocial insects suggest that kin discrimination during mate choice may be a more common mechanism in socially simpler species with no reproductive division of labour. Here we examined this possibility in the subsocial cockroach Nauphoeta cinerea, a model species for research in sexual selection, where males establish dominance hierarchies to access females and control breeding territories. When given a binary choice between a sibling male and a non-sibling male that had the opportunity to establish a hierarchy prior to the tests, females mated preferentially with the dominant male, irrespective of kinship or body size. Despite the lack of kin discrimination during mate choice, inbred-mated females incurred significant fitness costs, producing 20% less offspring than out-bred-mated females. We discuss how the social mating system of this territorial cockroach may naturally limit the probability of siblings to encounter and reproduce, without the need for evolving active inbreeding avoidance mechanisms, such as kin recognition.