The present register-based study investigated whether family social background modified the association between intelligence and unsuccessful educational and occupational achievement among young men in Denmark. The study population comprised all men born during the period from 1981 to 1991 who had appeared before a draft board until 2015 (N = 277,938). Family social background was measured by parental educational attainment at the birth of the study population. Intelligence was assessed by IQ scores on Børge Priens Prøve at age 18. Unsuccessful educational and occupational achievement were measured by no completed youth education at age 25, by no completed education leading to vocational qualifications at age 30, by not being in employment, education, or training (NEET) at age 30, and by gross income at age 30. Binary logistic regression and median regression were used to estimate the combined influence of family social background and IQ on unsuccessful educational and occupational achievement. The results showed that family social background modified the associations of IQ with risk of no youth education at age 25 and gross income at age 30, but the modifying influence seemed to depend on both the IQ level and the outcome indicator. Family social background was not found to modify the associations of IQ with risk of no vocational qualification at age 30 and risk of being NEET at age 30. In conclusion, the study findings suggest that several mechanisms might be at work in the complex and intertwined influences of family social background and intelligence on the risk of unsuccessful educational and occupational achievement.