Smart Grid is the next-generation intelligent power grid that maximizes energy efficiency with the convergence of IT technologies and the existing power grid. It enables consumers to check power rates in real time for active power consumption. It also enables suppliers to measure their expected power generation load, which stabilizes the operation of the power system. However, there are high possibility that various kinds of security threats such as data exposure, data theft, and privacy invasion may occur in interactive communication with intelligent devices. Therefore, to establish a secure environment for responding to such security threat with the smart grid, the key management technique, which is the core of the development of a security mechanism, is required. Using a hash chain, this paper suggests a group key management mechanism that is efficiently applicable to the smart grid environment with its hierarchical structure, and analyzes the security and efficiency of the suggested group key management framework.