Genome-wide association studies (GWAS) are among the workhorses of statistical genetics, having detected thousands of variants associated with complex traits and diseases. A typical GWAS examines the association between genotypes and the phenotype of interest while adjusting for a set of covariates. While covariates potentially have non-linear effects on the phenotype in many real world settings, due to the challenge of specifying the model, GWAS seldom include non-linear terms. Here we introduce DeepNull, a method that models non-linear covariate effects on phenotypes using a deep neural network (DNN) and then includes the model prediction as a single extra term in the GWAS association. First, using simulated data, we show that DeepNull increases statistical power by up to 20% while maintaining tight control of the type I error in the presence of interactions or non-linear covariate effects. Second, DeepNull maintains similar results to a standard GWAS when covariates have only linear effects on the phenotype. Third, DeepNull detects larger numbers of significant hits and loci (7% additional loci averaged over 10 traits) than standard GWAS in ten phenotypes from the UK Biobank (n=370K). Many of the hits found only by DeepNull are biologically plausible or have previously been reported in the GWAS catalog. Finally, DeepNull improves phenotype prediction by 23% averaged over the same ten phenotypes, the highest improvement was observed in the case of Glaucoma referral probability where DeepNull improves the phenotype prediction by 83%.