Fingertips positions play an important role in Human Computer Interaction. Traditional methods for fingertip detection, based on RGB images, are designed for stretched fingers only. Recent research, based on only depth images, could not perform well. In this paper, we propose a method for detecting and tracking the 3D position of a single fingertip, and recognizing its motion. Our algorithm is a fusion of 2D and depth detection. In order to promise the accuracy of detection and smooth the movement trajectory, a 3D Kalman filter is proposed. Finally, the hand motion is recognized based on the 3D coordinate sequences of the fingertips. Experiment results have demonstrated that the proposed method performs well because it can achieve an accuracy of 92.86% for fingertip detection.