Recent studies have shifted the attention on the beneficial role of psychological capital from workplace to academic contexts. Moreover, the mediating role of psychological capital in the effect of social support on student outcomes remains unknown. This topic has become more imperative under the pandemic. The current study aimed to investigate the impact of psychological capital on students’ well-being with family support as an antecedent and problem-focused coping as a mediator. Two hundred and eighty-one students completed the questionnaire at two time points. Results of the cross-lagged mediation analysis showed that family support positively predicted psychological capital, psychological capital positively predicted problem-focused coping, and problem-focused coping predicted well-being. Moreover, the chain mediation path between family support and well-being via psychological capital and problem-focused coping was significant. The current findings identify the antecedent and underlying mechanism behind the relationship between psychological capital and well-being, providing insights into psychological capital interventions for students.