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Variation in human cognitive ability is of consequence to a large number of health and social outcomes and is substantially heritable. Genetic linkage, genome-wide association, and copy number variant studies have investigated the contribution of genetic variation to individual differences in normal cognitive ability, but little research has considered the role of rare genetic variants. Exome sequencing studies have already met with success in discovering novel trait-gene associations for other complex traits. Here, we use exome sequencing to investigate the effects of rare variants on general cognitive ability. Unrelated Scottish individuals were selected for high scores on a general component of intelligence (g). The frequency of rare genetic variants (in n = 146) was compared with those from Scottish controls (total n = 486) who scored in the lower to middle range of the g distribution or on a proxy measure of g. Biological pathway analysis highlighted enrichment of the mitochondrial inner membrane component and apical part of cell gene ontology terms. Global burden analysis showed a greater total number of rare variants carried by high g cases versus controls, which is inconsistent with a mutation load hypothesis whereby mutations negatively affect g. The general finding of greater non-synonymous (vs. synonymous) variant effects is in line with evolutionary hypotheses for g. Given that this first sequencing study of high g was small, promising results were found, suggesting that the study of rare variants in larger samples would be worthwhile.