The computers are connected with each other by the network as a result of the progress of technology in the field of the computer and network, and then all of the data to be processed are transferred quickly and at the real-time through the computer network. However the user can use the computer system at any time, the user must go to the location of the computer system to use the computer resources. The necessities for using the computer system occur anywhere and anytime in spite of the location of the computer system. For this requirement the mobile computing environment (MCE) is expected strongly. In this paper we introduce the model of MCE and discuss the need of the user authentication at entering and logging-in the network in MCE only with a user ID. We propose the method of a user ID assignment from which a server ID can be decided by a simple logical operation. Also, we propose a protocol for a user authentication in MCE and discuss the robustness of security against the various attacking on the route.