Accurate and complete medical data are one valuable asset for patients. Privacy protection and the secure storage of medical data are crucial issues during medical services. Secure storage and making full use of personal medical records has always been a concern for the general population. The emergence of blockchain technology brings a new idea to solve this problem. As a hash chain with the characteristics of decentralization, verifiability and immutability, blockchain technology can be used to securely store personal medical data. In this paper, we design a storage scheme to manage personal medical data based on blockchain and cloud storage. Furthermore, a service framework for sharing medical records is described. In addition, the characteristics of the medical blockchain are presented and analyzed through a comparison with traditional systems. The proposed storage and sharing scheme does not depend on any third-party and no single party has absolute power to affect the processing.