Obesity and low cognitive function are associated with multiple adverse health outcomes across the life course. They have a small phenotypic correlation (r=-0.11; high body mass index (BMI)-low cognitive function), but whether they have a shared genetic aetiology is unknown. We investigated the phenotypic and genetic correlations between the traits using data from 6815 unrelated, genotyped members of Generation Scotland, an ethnically homogeneous cohort from five sites across Scotland. Genetic correlations were estimated using the following: same-sample bivariate genome-wide complex trait analysis (GCTA)-GREML; independent samples bivariate GCTA-GREML using Generation Scotland for cognitive data and four other samples (n=20 806) for BMI; and bivariate LDSC analysis using the largest genome-wide association study (GWAS) summary data on cognitive function (n=48 462) and BMI (n=339 224) to date. The GWAS summary data were also used to create polygenic scores for the two traits, with within- and cross-trait prediction taking place in the independent Generation Scotland cohort. A large genetic correlation of -0.51 (s.e. 0.15) was observed using the same-sample GCTA-GREML approach compared with -0.10 (s.e. 0.08) from the independent-samples GCTA-GREML approach and -0.22 (s.e. 0.03) from the bivariate LDSC analysis. A genetic profile score using cognition-specific genetic variants accounts for 0.08% (P=0.020) of the variance in BMI and a genetic profile score using BMI-specific variants accounts for 0.42% (P=1.9 × 10(-7)) of the variance in cognitive function. Seven common genetic variants are significantly associated with both traits at P<5 × 10(-5), which is significantly more than expected by chance (P=0.007). All these results suggest there are shared genetic contributions to BMI and cognitive function.Molecular Psychiatry advance online publication, 9 February 2016; doi:10.1038/mp.2015.205.