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Smart grid (SG) communication has recently received significant attentions to facilitate intelligent and distributed electric power transmission systems. However, communication trust and security issues still present practical concerns to the deployment of SG. In this paper, to cope with these challenging concerns, we propose a lightweight message authentication scheme features as a basic yet crucial component for secure SG communication framework. Specifically, in the proposed scheme, the smart meters which are distributed at different hierarchical networks of the SG can first achieve mutual authentication and establish the shared session key with Diffie-Hellman exchange protocol. Then, with the shared session key between smart meters and hash-based authentication code technique, the subsequent messages can be authenticated in a lightweight way. Detailed security analysis shows that the proposed scheme can satisfy the desirable security requirements of SG communications. In addition, extensive simulations have also been conducted to demonstrate the effectiveness of the proposed scheme in terms of low latency and few signal message exchanges.