Recently, radio-frequency identification (RFID) technology has been applied to various industrial fields. It is used for various health-care purposes such as patient information management and health management, thereby providing convenience for both hospital officials and patients. However, the RFID system also presents various health-care security threats such as spoofing attacks and counterfeit attacks in the data communication between the server, reader, and tag, which adversely affect both hospital officials and patients. An RFID mutual authentication technique is thus required, and various such techniques have already been proposed. Research is being conducted for performing RFID mutual authentication using bit operation or based on a lightweight public key cryptosystem for application to a low-cost tag environment. In this study, we analyze the RFID mutual authentication protocol for RFID medical devices and propose an efficient, lightweight mutual authentication scheme for secure RFID medical devices by satisfying various security requirements and decreasing the computation cost.