Group communications are significant applications of many emerging communication technologies. To preserve users' privacy in group communications, key agreement protocols with security and high efficiency are imperative. In this paper, a group key agreement protocol is presented to achieve this goal. The periodic array is originally applied to the group key agreement protocol to derive a session key by group members. Moreover, user authentication is supported in the proposed protocol to ensure secure group communications. Finally, the performance evaluation shows that the proposed protocol has both of the low communication complexity and the low computational complexity, indicating that the proposed protocol is efficient in group communications.