Over the last decade, with the increasing popularity and usage of the internet of things worldwide, Internet of Medical Things (IoMT) has emerged as a key technology of the modern era. IoMT uses Artificial Intelligence, 5G, big data, edge computing, and blockchain to provide users with electronic medical services. However, it may face several security threats and attacks over an insecure public network. Therefore, to protect sensitive medical data in IoMT, it is necessary to design a secure and efficient authentication protocol. In this study, we propose a privacy-preserving authentication management protocol based on blockchain. The protocol uses a blockchain to store identities and related parameters to assist communication entities in authentication. In addition, the protocol adopts a three-factor authentication method and introduces Chebyshev chaotic map to ensure the security of user login and authentication. Formal security proof and analysis using the random oracle model and Burrows-Abadi-Needham logic show that the proposed protocol is secure. Moreover, we use informal security analysis to demonstrate that the protocol can resist various security attacks. The functional comparison shows that the protocol has high security. Through performance analysis and comparison with other protocols, the proposed protocol can increase computation overhead, communication overhead, and storage overhead by up to 39.8%, 93.6%, and 86.7%,respectively. © 2023 Elsevier Ltd