Low-income populations are particularly susceptible to mental health problems, and the susceptibilities of family members may be interconnected. In particular, maternal factors are known to be linked to their children's outcomes. This study aims to investigate how maternal cognition, depression, and the mother-child relationship, as well as children's cognition, predict the mental health of children in low-income families. Pairs of mothers and children from families receiving governmental assistance were surveyed between January 2018 and March 2019. Korean versions of the following instruments were used: Strengths and Difficulties Questionnaire (children's mental health problems), Cognitive Triad Inventory for Children (children's cognition), Kerns' Security Scale (mother-child relationship), Center for Epidemiologic Studies Depression Scale (maternal depression), and Automatic Thoughts Questionnaire-Negative (maternal cognition). A structural equation model was used to examine how maternal cognition, depression, the mother-child relationship, and children's cognition predict children's mental health. Maternal negative cognition and depression mediated by the children's relationships with their mothers negatively predicted their cognition and mental health problems. Enhancing maternal mental health and a mother-child relationship can help improve positive cognition and mental health of children from low-income families.