Understanding the determinants of healthy mental ageing is a priority for society today. So far, we know that intelligence differences show high stability from childhood to old age and there are estimates of the genetic contribution to intelligence at different ages. However, attempts to discover whether genetic causes contribute to differences in cognitive ageing have been relatively uninformative. Here we provide an estimate of the genetic and environmental contributions to stability and change in intelligence across most of the human lifetime. We used genome-wide single nucleotide polymorphism (SNP) data from 1,940 unrelated individuals whose intelligence was measured in childhood (age 11 years) and again in old age (age 65, 70 or 79 years). We use a statistical method that allows genetic (co)variance to be estimated from SNP data on unrelated individuals. We estimate that causal genetic variants in linkage disequilibrium with common SNPs account for 0.24 of the variation in cognitive ability change from childhood to old age. Using bivariate analysis, we estimate a genetic correlation between intelligence at age 11 years and in old age of 0.62. These estimates, derived from rarely available data on lifetime cognitive measures, warrant the search for genetic causes of cognitive stability and change.