As the medical information systems continue to develop, the sharing of electronic medical records (EMRs) is becoming a vital tool for improving the quality and efficiency of medical services. However, during the process of sharing EMRs, establishing mutual-trust relationships and increasing users’ participation are urgent problems to be solved. Current solutions mainly focus on incentive mechanisms for users’ honest and active participation, but often ignore the potential impact of research institutions’ behavior on users’ trust and participation. To address this, this paper proposes an incentive mechanism based on evolutionary game theory. It combines the unchangeable nature of blockchain and the dynamic adjustment characteristics of evolutionary games to build a secure and trustworthy incentive system. This system considers the potential malicious behaviors of both users and research institutions, encouraging research institutions to protect users’ privacy, reduce users’ concerns, and guide users to actively contribute data. At the same time, it ensures data security and system trust through clear rewards and punishments. Based on this, we have carried out a comprehensive simulation using game theory. The results confirm that our designed incentive mechanism can effectively achieve its expected goals.