Background: Twin studies have shown that anxiety in a general population sample of children involves both domain-general and trait-specific genetic effects. For this reason, in an attempt to identify genes responsible for these effects, we investigated domain-general and trait-specific genetic associations in the first genome-wide association (GWA) study on anxiety-related behaviours (ARBs) in childhood. Methods: The sample included 2810 7-year-olds drawn from the Twins Early Development Study (TEDS) with data available for parent-rated anxiety and genome-wide DNA markers. The measure was the Anxiety-Related Behaviours Questionnaire (ARBQ), which assesses four anxiety traits and also yields a general anxiety composite. Affymetrix GeneChip 6.0 DNA arrays were used to genotype nearly 700,000 single-nucleotide polymorphisms (SNPs), and IMPUTE v2 was used to impute more than 1 million SNPs. Several GWA associations from this discovery sample were followed up in another TEDS sample of 4804 children. In addition, Genome-wide Complex Trait Analysis (GCTA) was used on the discovery sample, to estimate the total amount of variance in ARBs that can be accounted for by SNPs on the array. Results: No SNP associations met the demanding criterion of genome-wide significance that corrects for multiple testing across the genome (p<5×10-8). Attempts to replicate the top associations did not yield significant results. In contrast to the substantial twin study estimates of heritability which ranged from 0.50 (0.03) to 0.61 (0.01), the GCTA estimates of phenotypic variance accounted for by the SNPs were much lower 0.01 (0.11) to 0.19 (0.12). Conclusions: Taken together, these GWAS and GCTA results suggest that anxiety - similar to height, weight and intelligence - is affected by many genetic variants of small effect, but unlike these other prototypical polygenic traits, genetic influence on anxiety is not well tagged by common SNPs.