The COVID-19 pandemic has had substantial health, social, and economic effects on families. Consequent lockdowns and school closures heightened the burden on parents of school-age children. Many parents, while working from home, had to care for their children with restricted access to caregiver resources and to support their children’s education through homeschooling or remote learning provided by their schools. These duties created challenges and pressures on parents. Using online survey data collected from 197 parents of school-age (Prek-12) children during the first three months of the COVID-19 pandemic in the U.S., this preliminary study examined the relations among COVID-19-related stressors, including fear of COVID-19 and problems associated with school closures, parenting stress, and parental psychological well-being. Fear of COVID-19 and various issues associated with school closures were related to parenting stress and parental well-being. Parents with less instrumental and emotional support reported higher levels of parenting stress and lower levels of psychological well-being. The results of hierarchical multiple regressions revealed that parenting stress was the strongest predictor of parental psychological distress. Social support was associated with parental well-being but did not mediate the relation between parenting stress and parental well-being. The findings suggest that parenting stress during the COVID-19 lockdowns might take a toll on the mental health of parents of school-age children. Parents of school-age children need multiple layers of support, including targeted support addressing stressors related to school closures and parenting under quarantine.