This study investigated how parental depression, parental self-care, family conflict, and parental fear of COVID-19 are associated with children’s screen time during the COVID-19 pandemic. Data were collected online among South Korean families, resulting in 246 parents (59% fathers) with children between 6 and 12 years of age. Path analysis and multi-group structural equation modelling of fathers and mothers were conducted. Parent’s fear of COVID-19 was positively associated with parental depression. Parent’s fear of COVID-19 and parental depression were negatively related to parental self-care, which was negatively linked to family conflict. Family conflict was positively associated with children’s screen time. The relationships between parental factors and children’s screen time were different for mothers and fathers. Our results show that multiple family dynamics interact with children’s screen time, emphasizing the need to look beyond parenting practices in understanding the effects of COVID-19 pandemic on children’s screen time.