Recent analyses have shown educational attainment to be associated with a number of health outcomes. This association may, in part, be due to an effect of educational attainment on smoking behaviour. In this study, we apply a multivariable Mendelian randomisation design to determine whether the effect of educational attainment on smoking behaviour is due to educational attainment or general cognitive ability. We use individual data from the UK Biobank study (N = 120,050) and summary data from large GWA studies of educational attainment, cognitive ability and smoking behaviour. Our results show that more years of education are associated with a reduced likelihood of smoking that is not due to an effect of general cognitive ability on smoking behaviour. Given the considerable physical harms associated with smoking, the effect of educational attainment on smoking is likely to contribute to the health inequalities associated with differences in educational attainment.