Abstract Background Observational studies show an association between reduced lung function and impaired cognition. Cognitive dysfunction influences important health outcomes and is a precursor to dementia, but treatments options are currently very limited. Attention has therefore focused on identifying modifiable risk factors to prevent cognitive decline and preserve cognition. Our objective was to determine if lung function or risk of COPD causes reduced cognitive function using Mendelian randomization (MR). Methods Single nucleotide polymorphisms from genome wide association studies of lung function and COPD were used as exposures. We examined their effect on general cognitive function in a sample of 132,452 individuals. We then performed multivariable MR (MVMR), examining the effect of lung function before and after conditioning for covariates. Results We found only weak evidence that reduced lung function (Beta − 0.002 (SE 0.02), p-value 0.86) or increased liability to COPD (− 0.008 (0.008), p-value 0.35) causes lower cognitive function. MVMR found both reduced FEV₁ and FVC do cause lower cognitive function, but that after conditioning for height (− 0.03 (0.03), p-value 0.29 and − 0.01 (0.03) p-value 0.62, for FEV1 and FVC respectively) and educational attainment (− 0.03 (0.03) p-value 0.33 and − 0.01 (0.02), p-value 0.35) the evidence became weak. Conclusion We did not find evidence that reduced lung function or COPD causes reduced cognitive function. Previous observational studies are probably affected by residual confounding. Research efforts should focus on shared risk factors for reduced lung function and cognition, rather than lung function alone as a modifiable risk factor.