In this paper, we present context-aware home network environment on grid that controls the room appliances providing user mobility. The current home network technology (such as Havi, Jini and UPnP) is limited to a static local area. However, we propose ubiquitous concepts of home network system of user mobility in context-aware computing. It is called as CAHE-G which is not limited to static local area, but provides ubiquitous concepts of home network. CAHE-G controls home appliances according to context information, and is divided into two parts: Agent layer and Service layer. The Service layer consists of Lookup Service (LUS), Home Controller, Grid Service Provider (GridSP). The Service layer provides home and grid services with user request. LUS provides searching and registering those services. The Agent layer consists of Grid Agent (GA) and Home Context Agent (HCA). Grid technology can be used to automatically execute the home network service depending on context information. Agent layer provides user ubiquity, autonomous execution and large computation in this system. GA consists of Execution Manager (EM), MDS Manager (MM), and File Manager (FM) in order to enable those functionalities. Also, HCA provides autonomous adaptability to user. It gathers and interprets context information, then assigns the information to GA. As a result, in CAHE-G, Grid computing provides the capabilities: autonomous execution, interoperability, and the standard approaches to, and mechanisms for basic problems. Moreover, context-aware characteristic gives merits such as user mobility and adaptability.