Air quality prediction has received widespread attention from both the governments and citizens due to its close relation to our lives. Analyzing the spatial relations and temporal trends in air quality data is essential for air quality prediction task. However, most existing approaches require a pre-defined graph structure to capture the spatial dependencies of air quality data, and thus they can not be applied when a well-defined graph structure is unavailable. Besides, those methods do not give sufficient consideration to the latent relationships among entities of the graph over time. To overcome the above limitations, we propose a Spatial-Temporal Dynamic Graph Convolution Neural Network (ST-DGCN) in this paper. Our approach develops a dynamic adjacency matrix into graph convolution layer, which extracts the potential and time-varying spatial dependencies. To jointly model the spatial and temporal correlations, we combine dynamic graph convolution with gated recurrent unit and propose a unified DGC-GRU block. Next, a residual operation is further introduced into the DGC-GRU to simultaneously handle the information from different particles. Experimental results demonstrate that the proposed method outperforms the state-of-art baselines on two real-world air quality datasets.