Action recognition based on the 3D coordinates of body skeleton joints is an important topic in computer vision applications and human robot interaction. At present, most 3D data are captured using recently introduced economical depth sensors. In this study, we explore a new method for skeleton-based human action recognition. In this novel framework, the normalized angles of local joints are first extracted, and then the modified spherical harmonics (MSHs) are used to explicitly model the angular skeleton by projecting the spherical angles onto the unit sphere basis. This process decomposes the skeleton representation into a set of basis functions. A spatiotemporal system of the spherical angles is adopted to construct the static pose and joint displacement over a human action sequence. Consequently, the MSHs coefficients of the joints are used as the discriminative descriptor of the sequence. The extreme learning machine (ELM) classifier and recently published 3D action datasets are used to validate the proposed method. The experimental results show that the proposed approach performs better than many classical methods