The use of AI-based social robots has been shown to be beneficial for learning English as a Second Language (ESL). Not much is known, however, about the drivers of parental intention to use those robots in support of their children's ESL learning. This study aims to explore the factors that drive parental intention to adopt AI-based social robots for children's ESL learning. The research model is proposed based on the theories and literature regarding motivations, product smartness, personality traits and physical risk perception. Data collected from 315 participants are analyzed using the partial least squares structural equation modeling (PLS-SEM) method. The results show that utilitarian and hedonic motivations positively affect parental intention to adopt AI-based social robots. In addition, utilitarian motivation is influenced by robots' autonomy and parental personal innovativeness, while hedonic motivation is influenced by robots' autonomy and humanlike interaction, and parental personal innovativeness. From the findings, important implications for promoting parental intention to adopt AI-based social robots in children's ELS learning are offered.