Password-based authenticated group key exchange allows any group of users in possession of a low-entropy secret key to establish a common session key even in the presence of adversaries. In this paper, we propose a new generic construction of password-authenticated group key exchange protocol from any two-party password-authenticated key exchange with explicit authentication. Our new construction has several advantages when compared to existing solutions. First, our construction only assumes a common reference string and does not rely on any idealized models. Second, our scheme enjoys a simple and intuitive security proof in the universally composable framework and is optimal in the sense that it allows at most one password test per user instance. Third, our scheme also achieves a strong notion of security against insiders in that the adversary cannot bias the distribution of the session key as long as one of the players involved in the protocol is honest. Finally, we show how to easily extend our protocol to the dynamic case in a way that the costs of establishing a common key between two existing groups is significantly smaller than computing a common key from scratch.