Background Many studies have examined the negative impact on smartphone addiction in adolescents. Recent concerns have focused on predictors of smartphone addiction. This study aimed to investigate the association of adolescents’ smartphone addiction with family environment (specifically, domestic violence and parental addiction). We further investigated whether self-control and friendship quality, as predictors of smartphone addiction, may reduce the observed risk. Methods We used the 2013 national survey on internet usage and utilization data from the National Information Agency of Korea. Information on exposure and covariates included self-reported experience of domestic violence and parental addiction, sociodemographic variables, and other variables potentially related to smartphone addiction. Smartphone addiction was estimated using a smartphone addiction proneness scale, a standardized measure developed by national institutions in Korea. Results Adolescents who had experienced domestic violence (OR = 1.74; 95% CI: 1.23–2.45) and parental addiction (OR = 2.01; 95% CI: 1.24–3.27) were found to be at an increased risk for smartphone addiction after controlling for all potential variables. Furthermore, on classifying adolescents according to their level of self-control and friendship quality the association between domestic violence and parental addiction, and smartphone addiction was found to be significant in the group with adolescents with lower levels of self-control (OR = 2.87; 95% CI: 1.68–4.90 and OR = 1.95; 95% CI: 1.34–2.83) and friendship quality (OR = 2.33; 95% CI: 1.41–3.85 and OR = 1.83; 95% CI: 1.26–2.64). Conclusion Our findings suggest that family dysfunction was significantly associated with smartphone addiction. We also observed that self-control and friendship quality act as protective factors against adolescents’ smartphone addiction.