Based on innovation diffusion theory and self-determination theory, this study examines the interactions of undisclosed medical AI information on patients' acceptance of medical AI, discusses the mediating role of trust between them, and demonstrates the moderating mechanism of big five personality traits though analyzing 249 valid questionnaires. These questionnaires were conducted in China when COVID-19 broke out. The results indicate that the failure of information disclosure about medical AI has a significantly negative impact on patients' acceptance of medical AI, and patients' trust in medical AI plays a mediating role. The personality of openness to experience in big five personality traits negatively moderates the relationship between undisclosed medical AI information and patients' trust in medical AI. This study provides a significant reference value for the influence mechanism of undisclosed medical AI information on patients' acceptability, which could offer practical guidance for medical institutions to apply AI system.