Due to the extensive use of wireless technologies, security is one of the most important and challenging issues in smart grid networks. To secure data communications, strong authentication and key management mechanisms are needed. In this paper, we propose a mutual authentication scheme and key management protocol tailored for Home Area Network (HAN) with low overhead and enhanced robustness. Using identity-based cryptography technique, the proposed scheme broadcasts only a small packet to all HAN nodes to refresh their keys, thus significantly improving key management overhead cost by reducing network bandwidth. Analysis shows that the proposed scheme delivers required security against well-known HAN attacks, and can be easily adopted based on existing technologies.