This paper proposes a simple scheme for generating a three-atom GHZ state via cavity quantum electrodynamics (QED). The task can be achieved through the interaction between two EPR states, which can be prepared easily with current technology. In this scheme, the cavity field is only virtually excited during the interaction process, and no quantum information transfer between the atoms and the cavity is required. Thus it greatly prolongs the efficient decoherent time. Moreover, this scheme is also applicable for generating an .N-atom GHZ state.