Group Key Agreement (GKA) is a crypto-graphic primitive allowing two or more entities to negotiate a shared session key over public net-works. In existing GKA models, it is an open prob-lem to construct a one-round multi-party GKA pro-tocol. Wu et cd. recently proposed the concept of asymmetric group key agreement (ASGKA) and re-alized a one-round ASGKA protocol, which affirma-tively answers the above open problem in a relaxed way. However, the ASGKA protocol only applies to static groups. To fill this gap, this paper proposes an extended ASGKA protocol based on the Wu et al. protocol. The extension allows any member to join and leave at any point, provided that the resul-ting group size is not greater than n. To validate the proposal, extensive experiments are performed and the experimental results show that our protocol is more effective than a plain realization of the Wu et al. protocol for dynamic groups. The extended pro-tocol is also more efficient than the up-to-date dy-namic GKA protocol in terms of communication and computation.