the measurement of similarity between two motion trajectories is one of the fundamental task for motion analysis, perception and recognition. previous research focus on 2d trajectory similarity measurement. with the advent of 3d sensors, it is possible to collect large amounts of 3d trajectory data for more precise motion representation. as trajectories in 3d space may often exhibit a similar motion pattern but may differ in location, orientation, scale, and appearance variations, the trajectory descriptor must be invariant to these degrees of freedom. shape context is one of the rich local shape descriptors can be used to represent the trajectory in 2d space, however, rarely applied in the 3d motion trajectory recognition field. to handle 3d data, in this paper, we first naturally extend the shape context into the spatiotemporal domain by adopting a spherical neighborhood, and named it 3d shape context(3dsc). to achieve better global invariant on trajectories classification, the adaptive outer radius of 3dsc for extracting 3d shape context feature is proposed. the advantages of our proposed 3d shape context are: (1) it is invariant to motion trajectories translation and scale in the spatiotemporal domain; (2) it contains the whole trajectory points in the 3dsc ball volume, thus can achieve global information representation and is good for solving sub-trajectories problem; (3) it is insensitive to the appearance variations in the identical meaning trajectories, meanwhile, can greatly discriminate the distinct meaning trajectories. in trajectory recognition phase, we consider a feature-to-feature alignment between motion trajectories based on dynamic time warping and then use the one nearest neighbor (1nn) classifier for final accuracy evaluation. we test the performance of proposed 3d sc-dtw on uci asl large dataset, digital hand dataset and the experimental results demonstrate the effectiveness of our method.