This paper proposes a new graph convolutional operator called central difference graph convolution (CDGC) for skeleton based action recognition. It is not only able to aggregate node information like a vanilla graph convolutional operation but also gradient information. Without introducing any additional parameters, CDGC can replace vanilla graph convolution in any existing Graph Convolutional Networks (GCNs). In addition, an accelerated version of the CDGC is developed which greatly improves the speed of training. Experiments on two popular large-scale datasets NTU RGB+D 60 & 120 have demonstrated the efficacy of the proposed CDGC. Code is available at https://github.com/iesymiao/CD-GCN.