In this paper, we propose a new local descriptor for action recognition in depth images. Our proposed descrip-tor jointly encodes the shape and motion cues using surface normals in 4D space of depth, time, spatial coordinates and higher-order partial derivatives of depth values along spatial coordinates. In a traditional Bag-of-words (BoW) approach, local descriptors extracted from a depth sequence are encoded to form a global representation of the sequence. In our approach, local descriptors are encoded using Sparse Coding (SC) and Fisher Vector (FV), which have been recently proven effective for action recognition. Action recognition is then simply performed using a linear SVM classifier. Our proposed action descriptor is evaluated on two public benchmark datasets, MSRAction3D and MSRGesture3D. The experimental result shows the effectiveness of the proposed method on both the datasets.