Mobile ad hoc networks create additional challenges for implementing the group key establishment due to resource constraints on nodes and dynamic changes on topology. The nodes in mobile ad hoc networks are usually low power devices that run on battery power. As a result, the costs of the node resources should be minimized when constructing a group key agreement protocol so that the battery life could be prolonged. To achieve this goal, in this paper we propose a security efficient group key agreement protocol based on Burmester-Desmedt (BD) scheme and layer-cluster group model, referred to as LCKM-BD, which is appropriate for large mobile ad hoc networks. In the layer-cluster group model, BD scheme is employed to establish group key, which can not only meet security demands of mobile ad hoc networks but also improve executing performance. Finally, the proposed protocol LCKM-BD are compared with BD, TGDH (tree-based group Diffe-Hellman), and GDH (group Diffie-Hellman) group key agreement protocols. The analysis results show that our protocol can significantly decrease both the computational overhead and communication costs with respect to these comparable protocols.