Due to the current COVID-19 pandemic, colleges and universities have implemented network teaching. E-learning engagement is the most important concern of educators and parents because this will directly affect student academic performance. Hence, this study focuses on students’ perceived family support and their e-learning engagement and analyses the effects of e-learning normative consciousness and behaviours and self-efficacy on the relationship between family support and e-learning engagement in college students. Prior to this study, the relationship between these variables was unknown. Four (...) structural equation models revealed the multiple mediating roles of e-learning normative consciousness and behaviours and self-efficacy in the relationship between family support and e-learning engagement. A total of 1317 college students (mean age = 19.51; 52.2% freshman) voluntarily participated in our study. The results showed that e-learning normative consciousness and behaviours and self-efficacy played significant and mediating roles between students’ perceived family support and their e-learning engagement. Specifically, these two individual variables fully mediated the relationship between students’ perceived family support and their e-learning engagement. The multiple mediation model showed that family members can increase family support of their children by creating a household environment conducive to learning, displaying positive emotions, demonstrating the capability to assist their children, advocating the significance of learning normative consciousness and behaviours and encouraging dedicated and efficient learning. The findings complement and extend the understanding of factors influencing student e-learning engagement. (shrink)