Inbreeding depression refers to lower fitness among offspring of genetic relatives. This reduced fitness is caused by the inheritance of two identical chromosomal segments (autozygosity) across the genome, which may expose the effects of (partially) recessive deleterious mutations. Even among outbred populations, autozygosity can occur to varying degrees due to cryptic relatedness between parents. Using dense genome-wide single-nucleotide polymorphism (SNP) data, we examined the degree to which autozygosity associated with measured cognitive ability in an unselected sample of 4854 participants of European ancestry. We used runs of homozygosity - multiple homozygous SNPs in a row - to estimate autozygous tracts across the genome. We found that increased levels of autozygosity predicted lower general cognitive ability, and estimate a drop of 0.6 s.d. among the offspring of first cousins (P=0.003-0.02 depending on the model). This effect came predominantly from long and rare autozygous tracts, which theory predicts as more likely to be deleterious than short and common tracts. Association mapping of autozygous tracts did not reveal any specific regions that were predictive beyond chance after correcting for multiple testing genome wide. The observed effect size is consistent with studies of cognitive decline among offspring of known consanguineous relationships. These findings suggest a role for multiple recessive or partially recessive alleles in general cognitive ability, and that alleles decreasing general cognitive ability have been selected against over evolutionary time.