The digital development of electronic medical records has improved the accessibility and sharing of medical data and promoted the development of medical research institutions. However, when multiple institutions participate in the sharing at the same time, improper data access management makes patients not only face the risk of privacy disclosure, but also may lose the control of their own medical data. Therefore, we proposed a security sharing scheme for multi-institutional access control of medical data based on blockchain. Firstly, Shamir secret sharing technology was introduced to build a user key distribution mechanism, and through the distribution and recovery of key shares, the batch control of data access rights of multiple research institutions was realized, and the autonomy of patients on their own medical data was effectively maintained. Furthermore, the scheme integrates proxy re-encryption technology with key shares, creating a secure re-encryption framework. Trusted proxy nodes on the blockchain complete the conversion of medical ciphertexts, thereby enhancing the security of the medical data sharing process. Experimental results show that the proposed scheme effectively achieves fine-grained access control and improves data sharing security through the optimized proxy re-encryption technique, while keeping computational overhead within acceptable limits.