In Jeju Smart Grid field test, Zigbee technology is being used as one of customer side solutions for AMI. Although Zigbee networks that provides effective connectivity and control among devices are advantages in ease of implementation and use, the data can be exposed to cyber attacks such as eavesdrop, unauthorized data dissemination and forgery. Currently authentication and confidentiality services are provided with the network and link keys generated based on public key pairs that are pre-installed in offline. However, the network is vulnerable once a hacker intrudes into a local network because operation and management policies for the generated keys are not well-established yet. In this paper, the vulnerability of the Zigbee security system in the customer side environment of Jeju Smart Grid field test is analyzed. Then, two-way authentication with the unique identifiers of devices and user-specific group management policies are proposed to resolve the vulnerability.