The maintenance and sharing of electronic medical records are one of the essential tasks in the medical treatment combination. Traditional cloud-based electronic medical record storage system is difficult to realize data security sharing. The tamper resistance and traceability of blockchain technology provide the possibility for the sharing of highly sensitive medical data. This paper proposes a safe sharing scheme of stroke electronic medical records based on the consortium blockchain. The scheme adopts the storage method of ciphertext of medical records stored in the cloud and index of medical records stored on the blockchain. The privacy protection mechanism proposed in this paper innovatively combines proxy reencryption and searchable encryption which supports patient pseudoidentity search. The mechanism could achieve controllable sharing of medical records and precise search. According to the organizational characteristics of the stroke medical treatment combination, this paper proposes an improved Practical Byzantine Fault Tolerance mechanism to reach a consensus between consensus nodes. Then, the proposed scheme is analyzed and evaluated from three aspects of medical record integrity, user privacy, and data security. The results show that the scheme can not only ensure the privacy of patient identity information and private key data but also resist the tampering and deletion attacks of internal and external malicious nodes on the medical record data. Therefore, the proposed scheme is conducive to the improvement of the timeliness of stroke treatment and the safe sharing of electronic medical records in stroke medical treatment combination.