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Recently, Authentication protocol has been recognized as an important factor for grid computing security. This paper described a new simple and efficient Grid authentication system providing user anonymity. Our system is based on hash function, and mobile users only do symmetric encryption and decryption. In our system, it takes only one round of messages exchange between the mobile user and the visited network, and one round of message exchange between the visited network and the corresponding home network. The proposed architecture possesses several desirable emerging properties that enable it to provide an improved level of security for grid computing systems..