Smart grid is a new approach that significantly increases the efficiency of the entire electrical delivery system. The smart grid uses information technologies to improve how electricity travels from power plants to consumers, Allows consumers to interact with the grid and Integrates new and improved technologies into the operation of the grid. These techniques lead to some threats for the privacy of users. Since smart grid networks prepare detailed information and manage them to achieve a reliable network, such management might reveal users personal habits and behavior. The smart grid increases automation, continuity and coordination between consumers, suppliers and transmission network in long distance or local distribution networks. The development of a schema which is able to both satisfy requirements of the smart grid and guarantees the security of users has became a vast researchable area which is required a serious attention of the smart grid researchers and developers. The moving to a smart gird will depend to Meeting this challenge. We provide, via group signature, and efficient schema in order to preserve the users\\\' privacy. In the proposed schema SGGS, the data with high frequency are collected through the smart meters which have less computational overload, higher speed and so much less communication overhead than the previous schemas. In the schema SGGS, the group signature is used to make pseudonym and temporary short signature. The data confidentiality will be guaranteed through the random confidential keys, also the requirements, limitations and properties of the smart grid will be considered. In this case while the schema SGGS in having a high level of security, the cryptography overhead which is used to send the confidential data is much less than the previous schemas. Also we propose one batch verification schemes which double the efficiency of our schema

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