We propose a new human action recognition method based on quaternion three-dimensional (3D) skeleton representation,in order to accurately describe the movement details of human skeletons and 3D geometric relationship of skeletons. Firstly, we obtain skeletal sequences with the same frame quantity by applying linear interpolation and quadratic polynomial interpolation to normal key frames and variable key frames, respectively, on the basis of the captured key frames. Secondly, we use quaternions to represent 3D geometric skeletal relationship of the obtained skeletal sequences to generate quaternion feature descriptors. Finally, we use the support vector machine classifier to train and test the quaternion feature descriptors to realize recognition. Experimental results based on three standard datasets prove that the quaternion feature descriptor is robust to noise, changes of moving rate and viewpoint, and time domain misalignment, and it is able to improve the identification accuracy of human behavior significantly.