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Background Numerous studies have found associations between parental socio-economic position (SEP) and offspring asthma. Obesity and tobacco smoking during pregnancy (SDP) are more prevalent in lower SEP groups and have been identified as risk factors for childhood asthma.Aim The aim of this study was to explore and quantify the role of the modifiable risk factors—obesity, body mass index (BMI) and SDP—in the association between maternal SEP and offspring asthma.Methods This Swedish register-based cohort study included n=1 265 933 children born between 2006 and 2018, with information on asthma during the third and sixth years of life obtained from the National Patient Register and the Swedish Prescribed Drug Register. Maternal education was used as a measure of SEP. We used logistic regression to estimate exposure-outcome associations and applied the counterfactual approach to mediation analysis to estimate the proportion of the maternal SEP-offspring asthma association that could be explained by maternal obesity, BMI and SDP, with and without adjustment for birth year.Result The OR was 1.15 (95% CI 1.13 to 1.16) for the association between maternal education and asthma during the third year of life and slightly lower during the sixth year (OR 1.09, 95% CI 1.07 to 1.10). Out of the excess risks, 20%–30% could be explained by obesity or BMI through mediation and mediated interaction, while 15%–20% could be explained by SDP.Conclusion Our results indicate that supporting young women and mothers-to-be to healthy weight and to abstain from tobacco smoking, in particular during pregnancy, could reduce child morbidity and improve health equity in childhood.