Recently, communication in S mart G rid (SG) which causes to ease the smart transmission and distribution system has been dramatically taken in to consideration. In fact, reliable communication and security issues are considered as one of the main challenges in SG establishment. Security and privacy policy in future smart grid will have absolutely significant impact on their implementation and will be well-accepted by public. There are also vast researches to make sure smart conventional users of their safe information exchange. What is done and required in current electricity grid has a significant difference with telecom and internet networks. As an example, the ordinary meters of electricity or gas in A dvanced M easuring I nfrastructure (AMI), unlike telecom and internet networks, are devices with low functionality, using personal wireless network technology .e.g. (IEEE 802.15.4). This study tries to solve the rising concern and challenges by suggesting a safe protocol with small computational volume as a vital issue to safe SG community framework. What is especially considered in this suggested plan is that smart meters which were distributed hierarchically in different SG can reach to mutual Authentication and produce shared session key by using present data or energy consumption pattern. In order to use shared session key between smart meters (HAN GWs), and base station (BAN GW). The subsequent messages can be authenticated in a lightweight way. The security analysis shows that this project can fulfill the desired security requirements of SG communications. Besides, having small computation, it also consumes less energy. Keywords: Smart Grid, Smart Meter, Security, Privacy, Authentication