Recently, with rapid advances of mobile devices such as smart phone and wireless networking, a number of services using mobile device based wireless network have been explosively increasing. From the viewpoint of security, because wireless network is more vulnerable than wired network, strong security is required in wireless network. On the contrary, the security for mobile devices has to be efficient due to the restrictions of battery powered mobile device such as low computation, low memory space and high communication cost. Therefore, in this paper, we propose an efficient authentication scheme with mobile devices in wireless network environment. The proposed scheme satisfies security requirements for the service using mobile device and it is suitable in wireless network environment.