The consequence of reduced cognitive ability from inbreeding has long been investigated, mainly restricted to cousin–cousin marriages. Molecular genetic techniques now allow us to test the relationship between increased ancestral inbreeding and cognitive ability in a population of traditionally unrelated individuals. In a representative UK sample of 2329 individuals, we used genome-wide SNP data to estimate the percentage of the genome covered by runs of homozygous SNPs (ROH). This was tested for association with general cognitive ability, as well as measures of verbal and non-verbal ability. Further, association was tested between these traits and specific ROH. Burden of ROH was not associated with cognitive ability after correction for multiple testing, although burden of ROH was nominally associated with increased non-verbal cognitive ability (P=0.03). Moreover, although no individual ROH was significantly associated with cognitive ability, there was a significant bias towards increased cognitive ability in carriers of ROH (P=0.002). A potential explanation for these results is increased positive assortative mating in spouses with higher cognitive ability, although we found no evidence in support of this hypothesis in a separate sample. Reduced minor allele frequency across the genome was associated with higher cognitive ability, which could contribute to an apparent increase in ROH. This may reflect minor alleles being more likely to be deleterious.