The conventional electricity infrastructure relies on the usage of fossil fuels, which harms the environment greatly. A smart grid is an infrastructure that enables the integration of renewable resources with the distribution system, as well as the potential of establishing a two-way flow of energy and data between network management and subscribers in order to optimize energy use. However, this data flow may be misused by attackers to disrupt security and causes power network imbalances.Therefore, it is necessary to exploit different security protocols to exchange data in this platform. One of these security protocols is the authenticated key agreement protocol, which allows the parties to authenticate each other and share a key to encrypt data. Recently Zhang et al. proposed a lightweight key authentication protocol based on hash functions. In this paper, we examine their protocol and show that vulnerable to denial of service (DOS) attack and also is not optimized to implement on smart grid. Then we present a lightweight and secure authentication protocol based on hash functions.