Mobile ad hoc networks (MANETs) are self-configuring networks of wireless nodes, i.e., mobile devices. Since communications in MANETs occur via wireless channels, it is of significance to secure communications among wireless and mobile nodes. Group key management, as a widely used method for securing group communications, has potentially been used in MANETs for years. Most recently, a secure receiver-unrestricted group key management scheme for MANETs has been proposed, which is used to establish a secure channel among a group of wireless nodes without a trusted dealer, which has some advantages such as eliminating the certificate management problem and receiver restriction. However, a formal security analysis of this scheme is still lacking. Therefore, in this paper, we propose the complete security proof to demonstrate that the scheme satisfies the essential security properties including authentication, message confidentiality, known-key security and dynamic secrecy. We also give a brief discussion about the efficiency of the scheme.