Compared with traditional paper medical records, electronic medical records have many advantages such as easy transmission, high efficiency, better accuracy, and easier storage. The further development and penetration of electronic medical records will raise increasingly critical transmitted-data accuracy and security issues. Previous studies have proposed a verifier-based three-party authentication scheme and to provide high efficiency and security, with low computation and transmission costs. However, this protocol fails to achieve anonymity, is vulnerable to tracking attacks, and is inefficient. In this paper, we propose a new authentication scheme which provides patient anonymity and resistance to tracking attacks, while reducing computation and communication costs. The proposed system is easier to implement and is more suitable for use in remote electronic medical record exchange systems.