Inbreeding depression may be common in nature, reflecting either the failure of inbreeding avoidance strategies or inbreeding tolerance when avoidance is costly. The combined assessment of inbreeding risk, avoidance and depression is therefore fundamental to evaluate the inbreeding strategy of a population, that is how individuals respond to the risk of inbreeding. Here, we use the demographic and genetic monitoring of 10 generations of wild grey mouse lemurs (Microcebus murinus), small primates from Madagascar with overlapping generations, to examine their inbreeding strategy. Grey mouse lemurs have retained ancestral mammalian traits, including solitary lifestyle, polygynandry and male-biased dispersal, and may therefore offer a representative example of the inbreeding strategy of solitary mammals. The occurrence of close kin among candidate mates was frequent in young females (~37%, most often the father) and uncommon in young males (~6%) due to male-biased dispersal. However, close kin consistently represented a tiny fraction of candidate mates (< 1%) across age and sex categories. Mating biases favouring partners with intermediate relatedness were detectable in yearling females and adult males, possibly partly caused by avoidance of daughter–father matings. Finally, inbreeding depression, assessed as the effect of heterozygosity on survival, was undetectable using a capture–mark–recapture study. Overall, these results indicate that sex-biased dispersal is a primary inbreeding avoidance mechanism at the population level, and mating biases represent an additional strategy that may mitigate residual inbreeding costs at the individual level. Combined, these mechanisms explain the rarity of inbreeding and the lack of detectable inbreeding depression in this large, genetically diverse population.