Dispersal has a significant impact on lifetime reproductive success, and is often more prevalent in one sex than the other. In group-living mammals, dispersal is normally male-biased and in theory this sexual bias could be a response by males to female mate preferences, competition for access to females or resources, or the result of males avoiding inbreeding. There is a lack of studies on social mammals that simultaneously assess these factors and measure the fitness consequences of male dispersal decisions. Here we show that male-biased dispersal in the spotted hyaena (Crocuta crocuta) most probably results from an adaptive response by males to simple female mate-choice rules that have evolved to avoid inbreeding. Microsatellite profiling revealed that females preferred sires that were born into or immigrated into the female's group after the female was born. Furthermore, young females preferred short-tenured sires and older females preferred longer-tenured sires. Males responded to these female mate preferences by initiating their reproductive careers in groups containing the highest number of young females. As a consequence, 11% of males started their reproductive career in their natal group and 89% of males dispersed. Males that started reproduction in groups containing the highest number of young females had a higher long-term reproductive success than males that did not. The female mate-choice rules ensured that females effectively avoided inbreeding without the need to discriminate directly against close kin or males born in their own group, or to favour immigrant males. The extent of male dispersal as a response to such female mate preferences depends on the demographic structure of breeding groups, rather than the genetic relatedness between females and males.