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Fake news is spreading rapidly on social media and poses a serious threat to the COVID-19 outbreak response. This study thus aims to reveal the factors influencing the acceptance of fake news rebuttals on Sina Weibo. Drawing on the elaboration likelihood model (ELM), we used text mining and the econometrics method to investigate the relationships among the central route (rebuttal's information readability and argument quality), peripheral route (rebuttal's source credibility, including authority and influence), and rebuttal acceptance, as well as the moderating effect of receiver's cognitive ability on these relationships. Our findings suggest that source authority had a negative effect on rebuttal acceptance, while source influence had a positive effect. Second, both information readability and argument quality had positive effects on rebuttal acceptance. In addition, individuals with low cognitive abilities relied more on source credibility and argument quality to accept rebuttals, while individuals with high cognitive abilities relied more on information readability. This study can provide decision support for practitioners to establish more effective fake news rebuttal strategies; it is especially valuable to reduce the negative impact of fake news related to major public health emergencies and safeguard the implementation of anti-epidemic strategies.