Genome-wide association studies (GWAS) are hypothesis-free studies that estimate the association between polymorphisms across the genome with a trait of interest. To increase power and to estimate the direct effects of these single-nucleotide polymorphisms (SNPs) on a trait GWAS are often conditioned on a covariate (such as body mass index or smoking status). This adjustment can introduce bias in the estimated effect of the SNP on the trait. Two-sample Mendelian randomisation (MR) studies use summary statistics from GWAS estimate the causal effect of a risk factor (or exposure) on an outcome. Covariate adjustment in GWAS can bias the effect estimates obtained from MR studies conducted using covariate adjusted GWAS data. Multivariable MR (MVMR) is an extension of MR that includes multiple traits as exposures. Here we propose the use of MVMR to correct the bias in MR studies from covariate adjustment. We show how MVMR can recover unbiased estimates of the direct effect of the exposure of interest by including the covariate used to adjust the GWAS within the analysis. We apply this method to estimate the effect of systolic blood pressure on type-2 diabetes and the effect of waist circumference on systolic blood pressure. Our analytical and simulation results show that MVMR provides unbiased effect estimates for the exposure when either the exposure or outcome of interest has been adjusted for a covariate. Our results also highlight the parameters that determine when MR will be biased by GWAS covariate adjustment. The results from the applied analysis mirror these results, with equivalent results seen in the MVMR with and without adjusted GWAS. When GWAS results have been adjusted for a covariate, biasing MR effect estimates, direct effect estimates of an exposure on an outcome can be obtained by including that covariate as an additional exposure in an MVMR estimation. However, the estimated effect of the covariate obtained from the MVMR estimation is biased.