Prior research has indicated peer relationship problem as a risk factor in predicting Internet addiction among children and adolescents, while the underlying mechanism between this association remains largely unknown in current academia. This study examined the mediating role of fear of missing out in the relationship between peer relationship problems and Internet addiction and we further tested how family affective responsiveness would moderate the direct and indirect pathways. Based on a multistage random cluster sampling procedure, we recruited our participants (N = 2001) from one city in Hebei Province, China. Key variables were measured based on self-reported questionnaires for adolescents and data analysis was conducted by using Structural Equation Modeling (SEM). The results indicated that peer relationship problems were positively associated with Internet addiction. Besides, fear of missing out mediated the relationship between peer relationship problems and Internet addiction. Moreover, we found that family affective responsiveness moderated the indirect pathways between peer relationship problems and fear of missing out, as well as between fear of missing out and Internet addiction, with the effects being stronger for adolescents with a low level of family affective responsiveness compared with those with a high level of family affective responsiveness. However, family affective responsiveness failed to moderate the direct relationship between peer relationship problems and Internet addiction. Practical implications for future interventions were discussed according to the results given by our study.