Background: Smartphone addiction among children and adolescents has a negative effect, as excessive use of smartphones can cause physical symptoms, such as fatigue, indigestion, and sleep problems, as well as psychopathological problems, such as depression, anxiety, and impulsiveness. Materials and Methods: This study was carried out using the Korean Children and Youth Panel Survey 2019 conducted by the National Youth Policy Institute. The total number of participants was 4656 youths (2290 in grade 5 and 2366 in grade 8), and the dependent and independent variables were smartphone addiction in children and parents, respectively. Multiple regression analysis was conducted by Stata 15.0 SE. Results: First, the level of parents’ smartphone addiction affected that of children and adolescents. Second, the children’s and adolescents’ age affected the level of smartphone addiction, while their gender did not affect it. Third, the relationship between the levels of parents’ and children’s smartphone addiction was not moderated by the genders and ages of the children and adolescents. Conclusions: It was confirmed that as parents’ smartphone addiction increased, that of children increased, and smartphone addiction was found to increase in the second grade of middle school (12 years old) rather than grade 5 of elementary school (10 years old). Parents’ and children’s smartphone addiction was not moderated by children’s and adolescents’ gender and age.