Security and privacy are issues that cannot be ignored when collecting and processing medical data in the Internet of Medical Things (IoMT). Blockchain technology is a decentralized ledger system that has diverse application scenarios in the medical field. Blockchain technology relies on traditional cryptography to ensure data integrity and verifiability, but the creation of quantum computing has made it possible to break traditional encryption and signature methods. Therefore, quantum blockchain can provide a higher level of security for handling medical data. This paper innovatively designs a new medical data processing system based on quantum blockchain (QB-IMD). In QB-IMD, a quantum blockchain structure and a novel electronic medical record algorithm (QEMR) are proposed to ensure that the processed data is legitimate and tamper-proof. QEMR combines quantum signature and quantum identity authentication to avoid the potential security risks of digital signatures. In addition, through delegated computing by quantum cloud, medical diagnostic data can be computed without leaking to quantum cloud servers, thus protecting user privacy. Through mathematical proof, theoretical analysis and simulation, it is demonstrated that our scheme can resist six attacks and is feasible to protect user privacy. © IEEE