Introduction Children of parents with alcohol problems have been found to be at increased risk of adverse mental health outcomes. The aim was to test if there is a social gradient in emotional symptoms among young people with parental alcohol problems. We hypothesized that the shared burden of parental alcohol problems and low socioeconomic position would be associated with higher odds of frequent emotional symptoms. Methods Data came from Danish National Youth Study 2014, a web-based national survey, merged with register-data on family socioeconomic position. Participants consisted of 68,623 high school and vocational school students. Multilevel logistic regression models (nesting participants within 131 schools) were used to assess the association between perceived parental alcohol problems and frequent emotional symptom and effect-modification by financial strains in the family, family equivalent income or parental educational level. All analyses were adjusted for age, sex, education, immigration status, and cohabitation with parents. Results A higher proportion of young people from low socioeconomic position reported parental alcohol problems and young people with parental alcohol problems had higher odds of frequent emotional symptoms (OR = 1.50 95% CI: 1.41–1.60]), as compared to those without parental alcohol problems. Odds ratios for emotional symptoms were similar in strata of financial strains in the family; young people with parental alcohol problems and no financial strains in the family had an OR of 1.37 (95%CI: 1.26–1.49) and 1.33 (95% CI: 1.20–1.49) in those with financial strains in the family (P for interaction = 0.358). Same pattern was seen for parental educational level and family equivalent income. Conclusion Parental alcohol problems and low socioeconomic position were associated with higher odds of frequent emotional symptoms, but no sign of effect-modification by socioeconomic position was found.