Electronic medical records are vital and highly sensitive private information in medical data and need to be shared frequently between hospitals. Sharing medical data is considered a key method to improve the quality of medical services and reduce medical costs. However, electronic medical records are currently stored in different hospitals, which hinders the sharing of patient medical data and poses a serious threat to patient privacy. In order to solve these problems, a secure medical record sharing scheme based blockchain (SMRSBC) is proposed. In SMRSBC, the original EMR is securely stored in the cloud storage server, and the index is kept in the tamper-resistant alliance blockchain. This means that the risk of medical data leakage can be greatly reduced, and at the same time, the index in the blockchain ensures that the EMR cannot be arbitrarily modified. Through the patient's predefined access rights, the secure sharing of electronic medical data can be automatically completed through smart contracts on the blockchain. In addition, the use of elliptic curve encryption and asymmetric encryption technology in the patient's electronic medical data storage and extraction phases can protect the patient's privacy well. Analysis shows that SMRSBC is a safe and effective method to realize EMR data sharing.