Two-way communication has been identified as the smart grid flagship feature that enables the smart grid to attain its outcomes over the legacy power grid. Integrating communication networks into the power grid will motivate malicious attackers to target information exchange. Therefore, achieving secure and authentic communication in the smart grid networks is an indispensable requirement. In this paper, we propose a sophisticated hybrid encryption scheme that incorporates public and symmetric key encryptions to secure smart metering network. Elliptic Curve Integrated Encryption Scheme (ECIES) and Advanced Encryption Scheme (AES) are chosen as the building blocks for the proposed scheme. In order to optimize the computation overhead of ECIES, a precomputation procedure is presented to provide faster encryption/decryption. The proposed technique provides data integrity, confidentiality and authenticity as well as it resists against false data injection and message reply attacks. Simulation results show that the proposed approach surpasses some of the existing schemes in terms of computation, communication and storage overhead.