Background: The observed association between the parental socioeconomic status (SES, measured as education/income) and asthma or wheezing in offspring may be explained by confounding of unmeasured factors (shared genes and family environment). We aimed to study the association between parental SES and asthma/wheeze using cousin comparison. Method: Data were collected on individuals born in Sweden 2001–2013. Parental SES (education and income) was gathered from Statistics Sweden. Asthma/wheeze was identified using national health registers. The association between parental SES at birth and incident asthma/wheeze was estimated using Cox regression also comparing differently exposed cousins. The association between parental SES at 5 years and current asthma was estimated using logistic regression. Results: Included were 955,371 individuals. Mothers with compulsory school only (lowest education group) compared with those with further education (highest education group) was associated with incident asthma/wheeze below 1 year of age HRadj = 1.45 (1.38–1.52) and over 1 year of age HRadj = 1.17 (1.13–1.20). The corresponding estimates for the lowest income group were HRadj = 1.61 (1.54–1.69) and HRadj = 0.94 (0.92–0.97), respectively. In maternal cousin comparisons, the associations for asthma/wheeze over 1 year of age was HRadj = 1.21 (1.05–1.40) for compulsory school only and HRadj = 0.94 (0.84–1.07) for the lowest income group. The ORadj for current asthma at 5 years was 1.05 (1.00–1.11) for mother's compulsory school only and 0.98 (0.94–1.02) for mother's lowest income group. Results for estimates were similar for father's SES. Conclusion: We confirm an association between low parental SES (measured as education) and asthma/wheeze. Cousin comparison suggests that this association is not wholly due to confounding of unknown familial factors, therefore supporting a causal relationship. The relationship between parental income and asthma/wheeze is less clear. This study is important for understanding risk factors for asthma/wheeze and for future prevention strategies. Further research is warranted to investigate the possible mechanisms for association between parental education and asthma/wheeze.