General cognitive ability (g), which refers to what cognitive abilities have in common, is an important target for molecular genetic research because multivariate quantitative genetic analyses have shown that the same set of genes affects diverse cognitive abilities as well as learning disabilities. In this first autosomal genome-wide association scan of g, we used a two-stage quantitative trait locus (QTL) design with pooled DNA to screen more than 500 000 single nucleotide polymorphisms (SNPs) on microarrays, selecting from a sample of 7000 7-year-old children. In stage 1, we screened for allele frequency differences between groups pooled for low and high g. In stage 2, 47 SNPs nominated in stage 1 were tested by individually genotyping an independent sample of 3195 individuals, representative of the entire distribution of g scores in the full 7000 7-year-old children. Six SNPs yielded significant associations across the normal distribution of g, although only one SNP remained significant after a false discovery rate of 0.05 was imposed. However, none of these SNPs accounted for more than 0.4% of the variance of g, despite 95% power to detect associations of that size. It is likely that QTL effect sizes, even for highly heritable traits such as cognitive abilities and disabilities, are much smaller than previously assumed. Nonetheless, an aggregated ‘SNP set’ of the six SNPs correlated 0.11 (P < 0.00000003) with g. This shows that future SNP sets that will incorporate many more SNPs could be useful for predicting genetic risk and for investigating functional systems of effects from genes to brain to behavior.