Health risk factors such as body mass index (BMI), serum cholesterol and blood pressure are associated with many common diseases. It often remains unclear whether the risk factors are cause or consequence of disease, or whether the associations are the result of confounding.Genetic methods are useful to infer causality because genetic variants are present from birth and therefore unlikely to be confounded with environmental factors. We develop and apply a method (GSMR) that performs a multi-SNP Mendelian Randomization analysis using summarylevel data from large genome-wide association studies (sample sizes of up to 405,072) to test the causal associations of BMI, waist-to-hip ratio, serum cholesterols, blood pressures, height and years of schooling (EduYears) with a range of common diseases. We identify a number of causal associations including a protective effect of LDL-cholesterol against type-2 diabetes (T2D) that might explain the side effects of statins on T2D, a protective effect of EduYears against Alzheimer's disease, and bidirectional associations with opposite effects (e.g. higher BMI increases the risk of T2D but the effect T2D of BMI is negative). HDL-cholesterol has a significant risk effect on age-related macular degeneration, and the effect size remains significant accounting for the other risk factors. Our study develops powerful tools to integrate summary data from large studies to infer causality, and provides important candidates to be prioritized for further studies in medical research and for drug discovery.