Emerging technologies change the qualities of modern healthcare by employing smart systems for patient monitoring. To well use the data surrounding the patient, tiny sensing devices and smart gateways are involved. These sensing systems have been used to collect and analyze the real-time data remotely in Internet of Medical Thinks (IoM). Since the patient sensed information is so sensitive, the security and privacy of medical data are becoming challenging problem in IoM. It is then important to ensure the security, privacy and integrity of the transmitted data by designing a secure and a lightweight authentication protocol for the IoM. In this paper, in order to improve the authentication and communications in health care applications, we present a novel secure and anonymous authentication scheme. We will use elliptic curve cryptography (ECC) with random numbers generated by fuzzy logic. We simulate IoM scheme using network simulator 3 (NS3) and we employ optimized link state routing protocol (OLSR) algorithm and ECC at each node of the network. We apply some attack algorithms such as Pollard’s ρ and Baby-step Giant-step to evaluate the vulnerability of the proposed scheme.