Recognizing hand gestures from the video sequence acquired by a dynamic camera could be a useful interface between humans and mobile robots. We develop a state based approach to extract and recognize hand gestures from moving camera images. We improved Human-Following Local Coordinate (HFLC) System, a very simple and stable method for extracting hand motion trajectories, which is obtained from the located human face, body part and hand blob changing factor. Condensation algorithm and PCA-based algorithm was performed to recognize extracted hand trajectories. In last research, this Condensation Algorithm based method only applied for one person's hand gestures. In this paper, we propose a principal component analysis (PCA) based approach to improve the recognition accuracy. For further improvement, temporal changes in the observed hand area changing factor are utilized as new image features to be stored in the database after being analyzed by PCA. Every hand gesture trajectory in the database is classified into either one hand gesture categories, two hand gesture categories, or temporal changes in hand blob changes. We demonstrate the effectiveness of the proposed method by conducting experiments on 45 kinds of sign language based Japanese and American Sign Language gestures obtained from 5 people. Our experimental recognition results show better performance is obtained by PCA based approach than the Condensation algorithm based method.