The elderly population is increasing rapidly all over the world. One major risk for elderly people is fall accidents, especially for those living alone. In this paper, we propose a robust fall detection approach by analyzing the tracked key joints of the human body using a single depth camera. Compared to the rivals that rely on the RGB inputs, the proposed scheme is independent of illumination of the lights and can work even in a dark room. In our scheme, a pose-invariant randomized decision tree algorithm is proposed for the key joint extraction, which requires low computational cost during the training and test. Then, the support vector machine classifier is employed to determine whether a fall motion occurs, whose input is the 3-D trajectory of the head joint. The experimental results demonstrate that the proposed fall detection method is more accurate and robust compared with the state-of-the-art methods.