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Rapid development of computer technology has brought a great change in our lives.According to spread of smart devices, a new input device has been required.The hand gesture recognition is one of hot topics in field of Human Computer Interaction (HCI).Our main purpose is to improve the gesture recognition rate and propose a more accurate method of hand gesture recognition that can satisfy the requirements of HCI.The speech-impaired people use the hand gestures of sign language as a tool of communication.Hand gesture recognition system can be used for interfacing between computer and human using hand gesture.The main content is divided into three parts.The first part is to research the novel method to extract robust geometric features.In our framework, the hand region is extracted from the background with the background subtraction method and HSV color space.Then, the palm and fingers are segmented so as to detect and recognize the fingers.After the finger segmentation processing, the fingertip points, finger-start points, palm center and wrist center points are obtained as a geometric features.When the fingers are detected and recognized, the hand gesture can be recognized by using a simple rule classifier and shows 96.6％ recognition accuracy.In the second part, hand geometric features are used to regroup the sign gestures and recognition of ASL finger spelling gestures.There are 24 static gestures in American Sign Language, and it can be subdivided into 4 groups by finger segmentation method.To recognize the inner hand texture information, histogram of oriented gradient method is used.For each gesture, 200 images are captured to training and 100 images are captured to analyze recognition rate.In the test part, our proposed method shows 97.79％ recognition accuracy.In the third part, we proposed the method of dynamic hand gesture recognition by using 8 direction chain strokes and crossing count method.The chain strokes method is used to calculate moving direction of fingertip point.The crossing count mask monitors 8 pixels that surround the fingertip point in every motion.In the final stage, we implemented augmented reality in hand detection method.