There is evidence across several species for genetic control of phenotypic variation of complex traits, such that the variance among phenotypes is genotype dependent. Understanding genetic control of variability is important in evolutionary biology, agricultural selection programmes and human medicine, yet for complex traits, no individual genetic variants associated with variance, as opposed to the mean, have been identified. Here we perform a meta-analysis of genome-wide association studies of phenotypic variation using approximately 170,000 samples on height and body mass index (BMI) in human populations. We report evidence that the single nucleotide polymorphism (SNP) rs7202116 at the FTO gene locus, which is known to be associated with obesity (as measured by mean BMI for each rs7202116 genotype), is also associated with phenotypic variability. We show that the results are not due to scale effects or other artefacts, and find no other experiment-wise significant evidence for effects on variability, either at loci other than FTO for BMI or at any locus for height. The difference in variance for BMI among individuals with opposite homozygous genotypes at the FTO locus is approximately 7%, corresponding to a difference of approximately 0.5 kilograms in the standard deviation of weight. Our results indicate that genetic variants can be discovered that are associated with variability, and that between-person variability in obesity can partly be explained by the genotype at the FTO locus. The results are consistent with reported FTO by environment interactions for BMI, possibly mediated by DNA methylation. Our BMI results for other SNPs and our height results for all SNPs suggest that most genetic variants, including those that influence mean height or mean BMI, are not associated with phenotypic variance, or that their effects on variability are too small to detect even with samples sizes greater than 100,000.