The study aimed to investigate behavioural intentions to receive free and self-paid COVID-19 vaccinations (BICV-F and BICV-SP) among Chinese university students if the vaccine was 80% effective with rare mild side effects, to examine their associations with social media exposures and peer discussions regarding COVID-19 vaccination, and to explore the mediational role of perceived information sufficiency about COVID-19 vaccination. An online anonymous survey (N = 6922) was conducted in November 2020 in five Chinese provinces. Logistic regression and path analysis were adopted. The prevalence of BICV-F and BICV-SP were 78.1% and 57.7%. BICV-F was positively associated with the frequencies of passive social media exposure (adjusted odds ratio (AOR) = 1.32, P < 0.001), active social media interaction (AOR = 1.13, P < 0.001) and peer discussions (AOR = 1.17, P < 0.001). Indirect effects of the three factors on BICV-F via perceived information sufficiency were all significant (P < 0.001). The direct effect of active social media interaction on BICV-F was significantly negative (P < 0.001). Similar associations/mediations were observed for BICV-SP. The COVID-19 vaccination intention of Chinese university students needs improvement. Boosting social media exposures and peer discussions may raise students' perceived information sufficiency and subsequently increase their vaccination intention. Considering the potential negative effect of active social media interaction, caution is needed when using social media to promote COVID-19 vaccination.