In this paper, we propose a novel two-level hierarchical framework for three-dimensional (3D) skeleton-based action recognition, in order to tackle the challenges of high intra-class variance, movement speed variability and high computational costs of action recognition. In the first level, a new part-based clustering module is proposed. In this module, we introduce a part-based five-dimensional (5D) feature vector to explore the most relevant joints of body parts in each action sequence, upon which action sequences are automatically clustered and the high intra-class variance is mitigated. In the second level, there are two modules, motion feature extraction and action graphs. In the module of motion feature extraction, we utilize the cluster-relevant joints only and present a new statistical principle to decide the time scale of motion features, to reduce computational costs and adapt to variable movement speed. In the action graphs module, we exploit these 3D skeleton-based motion features to build action graphs, and devise a new score function based on maximum-likelihood estimation for action graph-based recognition. Experiments on the Microsoft Research Action3D dataset and the University of Texas Kinect Action dataset demonstrate that our method is superior or at least comparable to other state-of-the-art methods, achieving 95.56% recognition rate on the former dataset and 95.96% on the latter one.