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In this paper, we proposed a hand gesture recognition system for Human Computer Interaction purposes. We first adopted AdaBoost algorithm to detect the user's hand automatically from the video stream which is based on Haar-like features as the representation of hand gestures. Then, a Multi-class Support Vector Machines was used to training and recognition the hand gesture based on the Hu invariant moments features. Finally, the Human Computer Conversation in the manner of hand gesture interaction instead of traditional mouse and keyboard was implemented.