Enterprise Architecture (EA) has been widely applied to Information systems. As Information Systems deployed into society, application domains of EA also extended. For example, The Open Group Architecture Framework (TOGAF) has been extended to include Physical Architecture layer. It is necessary to develop an EA design method for real-time systems such as automobile cars which consist of embedded devices. In this paper, we propose an Enterprise Application Architecture design approach for real-time systems based on the Hatley Pirbhai method using ArchiMate. Furthermore, we conduct a case study of applying this approach to an automobile management system.