Graph Convolutional Networks (GCNs) have been widely used in skeleton-based human action recognition. In GCN-based methods, the spatio-temporal graph is fundamental for capturing motion patterns. However, existing approaches ignore the physical dependency and synchronized spatio-temporal correlations between joints, which limits the representation capability of GCNs. To solve these problems, we construct the directed diffusion graph for action modeling and introduce the activity partition strategy to optimize the weight sharing mechanism of graph convolution kernels. In addition, we present the spatio-temporal synchronization encoder to embed synchronized spatio-temporal semantics. Finally, we propose Directed Diffusion Graph Convolutional Network (DD-GCN) for action recognition, and the experiments on three public datasets: NTU-RGB+D, NTU-RGB+D 120, and NW-UCLA, demonstrate the state-of-the-art performance of our method.