Children's addiction to smartphones has become a serious issue, and parental mediation could help prevent children's problematic use of smartphones. This research examined the factors that predict and explain parents' intention to mediate children's behavior over smartphone use. Based on a survey of 460 parents of elementary school students, we found that parental mediation was predicted by (a) parent's own addiction to smartphones, (b) perceived severity of smartphone addiction, and (c) personality traits such as neuroticism, openness, and agreeableness. To the best of our knowledge, this study is the first to examine the predictors of parental mediation regarding children's smartphone addiction, and the findings suggest some strategies to increase parental mediation.