Context-aware application plays an important role in ubiquitous computing (ubiComp) environment by providing user with anytime, anywhere services even without any explicitly triggered command. In this paper we propose a unified context-aware application model which is an essential part to develop various applications in ubiquitous computing environment. The proposed model affirms the independence between sensor and application by using unified context in the form of 5W1H. It also ensures that application exploits relatively accurate context to trigger personalized services. To show usefulness of the proposed model, we apply it to the sensors and applications in the ubiHome, a test bed for ubiComp-enabled home applications. According to the experimental results, without loss of generality, we believe it can be extended to various context-aware applications in daily life.