Motion trajectory recognition is one of the most important means to determine the identity of a moving object. A compact and discriminative feature representation method can improve the trajectory recognition accuracy. This paper presents an efficient framework for action recognition using a three-dimensional skeleton kinematic joint model. First, we put forward a rotation-scale-translation-invariant shape descriptor based on point context (PC) and the normal vector of hypersurface to jointly characterize local motion and shape information. Meanwhile, an algorithm for extracting the key trajectory based on the confidence coefficient is proposed to reduce the randomness and computational complexity. Second, to decrease the eigenvalue decomposition time complexity, a tensor shape descriptor (TSD) based on PC that can globally capture the spatial layout and temporal order to preserve the spatial information of each frame is proposed. Then, a multilinear projection process is achieved by tensor dynamic time warping to map the TSD to a low-dimensional tensor subspace of the same size. Experimental results show that the proposed shape descriptor is effective and feasible, and the proposed approach obtains considerable performance improvement over the state-of-the-art approaches with respect to accuracy on a public action dataset.