Secure group communication is an active area of research and its popularity is fuelled by the growing importance of group-oriented applications such as teleconferences, collaborative workspace, pay per-view etc. A number of group key agreement protocols have been proposed for these objectives. However most of the protocols have not considers the anonymity of the participants. Although in some applications the privacy of member's identity becomes more crucial and urgent especially for mobile users of a wireless network due to the open nature of radio media. The protocols having complex computations like large modular exponentiations, pairing computations, etc. are not well suited in wireless environments. Hence this paper proposes an anonymous ID-based group key agreement protocol without bilinear pairings. The proposed protocol also have anonymous join and leave procedures to facilitates the dynamic group operations. Security and performance analysis of proposed protocol shows that it provides strong security protection under different security attributes, and needs comparatively less computation and communication overheads than the other existing protocols. In addition the formal security verification of proposed protocol has been done by using AVISPA tool which shows that it is unforgeable against active and passive attacks.