In this paper a gesture recognition system using 3D data is described. The system relies on a novel 3D sensor that generates a dense range image of the scene. The main novelty of the proposed system, with respect to other 3D gesture recognition techniques, is the capability for robust recognition of complex hand postures such as those encountered in sign language alphabets. This is achieved by explicitly employing 3D hand features. Moreover, the proposed approach does not rely on colour information, and guarantees robust segmentation of the hand under various illumination conditions, and content of the scene. Several novel 3D image analysis algorithms are presented covering the complete processing chain: 3D image acquisition, arm segmentation, hand-forearm segmentation, hand pose estimation, 3D feature extraction, and gesture classification. The proposed system is tested in an application scenario involving the recognition of sign-language postures.