Background: Exposure to parental substance use problems has been associated with offsprings poor health and adverse social outcomes. In this study, we examined the association between exposure to parental substance use disorder (SUD) during childhood, and adolescence and offspring psychiatric conditions in young adulthood. Method: This was a register-based cohort study comprising 562,095 males and 531,130 females born between 1981 and 1990 in Sweden. Parental SUD was captured between the offspring's birth and eighteenth birthday. Cox regression models were used to estimate the Hazard Ratio (HR) of psychiatric conditions from age 18 years to a maximum age of 35 years, from January 1, 1999 to December 31, 2016. Results: About 4% of the study population was exposed to parental SUD during childhood and adolescence. The HR of psychiatric diagnosis was higher in males (1.80, 95% CI = 1.77–1.85) and females (1.56, 95% CI = 1.51–1.60) who were exposed to parental SUD, compared to those who were not; after adjusting for year of birth, domicile, origin, relative poverty, and other parental psychiatric diagnoses. The risks of psychiatric conditions were higher among males and females exposed to parental SUD during childhood compared to during adolescence. Conclusion: Exposure to parental SUD during childhood and adolescence was associated with an increased risk of psychiatric conditions in early adulthood for both males and females. Neither origin, poverty, municipality, or other parental psychiatric diagnoses fully explained the association. These risks seemed to be somewhat higher among males, and among those exposed during childhood when compared to during adolescence.