Mendelian Randomization (MR) has been widely applied to infer causality of exposures on outcomes in the genome wide association (GWAS) era. Existing approaches are often subject to biases from multiple sources including weak instruments, sample overlap, and measurement error. We introduce MRBEE, a computationally efficient multivariable MR method that can correct for all known biases simultaneously, which is demonstrated in theory, simulations, and real data analysis. In comparison, all existing MR methods are biased. In two independent real data analyses, we observed that the causal effect of BMI on coronary artery disease risk is completely mediated by blood pressure, and that existing MR methods drastically underestimate the causal effect of cannabis use disorder on schizophrenia risk compared to MRBEE. We demonstrate that MRBEE can be a useful tool in studying causality between multiple risk factors and a disease outcome, especially as more GWAS summary statistics are being made publicly available.