In this paper, we propose a robust fingertip extraction and extended Continuously Adaptive Mean Shift (CAMSHIFT) based robust hand gesture recognition for natural human-like HRI (Human-Robot Interaction). Firstly, for efficient and rapid hand detection, the hand candidate regions are segmented by the combination with robust $YC_bC_r$ skin color model and haar-like features based adaboost. Using the extracted hand candidate regions, we estimate the palm region and fingertip position from distance transformation based voting and geometrical feature of hands. From the hand orientation and palm center position, we find the optimal fingertip position and its orientation. Then using extended CAMSHIFT, we reliably track the 2D hand gesture trajectory with extracted fingertip. Finally, we applied the conditional density propagation (CONDENSATION) to recognize the pre-defined temporal motion trajectories. Experimental results show that the proposed algorithm not only rapidly extracts the hand region with accurately extracted fingertip and its angle but also robustly tracks the hand under different illumination, size and rotation conditions. Using these results, we successfully recognize the multiple hand gestures.