This study examined the relationship between variables about family members co-residing during the COVID-19 pandemic and anxiety about COVID-19, domestic violence from spouse, child abuse anxiety, internet addiction, and mental health as social problems related to the COVID-19 pandemic. A total of 220 parents (70 male and 150 female, age; M = 41.6, SD = 34.4) were included in the analysis. Stepwise hierarchical multiple regression analysis was conducted with dependent variables of fear of COVID-19, spousal violence, anxiety regarding perpetrating child abuse, internet addiction, and mental health. The independent variables were basic variables related to family members such as family composition. The results demonstrated that parents with preschool children were anxious about the possibility that they might abuse their children (β = .203, p < .01). Subjects who smoked were associated with anxiety about being the victim of domestic violence by their spouse (β = .154, p < .05). Those whose income had decreased due to the COVID-19 pandemic, those who were employed, and those with few rooms in their house were more likely to be dependent on the Internet (in order, β = .189, p < .01; β = .196, p < .01; β = -.140, p < .05). Finally, mental health was impaired among those whose income was reduced by the COVID-19 pandemic (β = .134, p < .05) and among those who had conflicting opinions in their families regarding the pandemic (β = .206, p < .01). These results indicate that family variables are associated with family social problems. Additionally, we assume these have been exacerbated by the COVID-19 pandemic. While further research is required to determine the causal relationships among the variables, the findings can be used as an indicator of support that should be provided to families.