Parental food education has been recognized among the important factors influencing children’s food literacy; however, the intrinsic mechanisms through which this influence occurs are unclear. In this study, a mediation model was constructed to explore this issue, using the parent–child relationship and learning motivation as mediating variables. In total, 204 children, aged 9–14 years old, responded to questionnaires on parental food education, children’s food literacy, the parent–child relationship, and learning motivation, which were used to measure the variables of interest. The results showed that parental food education was significantly and positively related to the parent–child relationship, learning motivation, and children’s food literacy; the parent–child relationship was significantly and positively related to learning motivation; and learning motivation was significantly and positively related to children’s food literacy. Parental food education influenced children’s food literacy in the following two main ways: the mediating role of learning motivation and the chain-mediating roles of the parent–child relationship and learning motivation. In addition, we attempt to explore the moderating role of the teaching stage between parental food education and the parent–child relationship, learning motivation, and children’s food literacy. In this paper, we discuss possible guidelines for family food education and children’s health based on the findings of the current study.