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Disease diagnosis on chest X-ray images is a challenging multi-label classification task. Previous works generally classify the diseases independently on the input image without considering any correlation among diseases. However, such correlation actually exists, for example, Pleural Effusion is more likely to appear when Pneumothorax is present. In this work, we propose a Disease Diagnosis Graph Convolutional Network (DD-GCN) that presents a novel view of investigating the inter-dependency among different diseases by using a dynamic learnable adjacency matrix in graph structure to improve the diagnosis accuracy. To learn more natural and reliable correlation relationship, we feed each node with the image-level individual feature map corresponding to each type of disease. To our knowledge, our method is the first to build a graph over the feature maps with a dynamic adjacency matrix for correlation learning. To further deal with a practical issue of incomplete labels, DD-GCN also utilizes an adaptive loss and a curriculum learning strategy to train the model on incomplete labels. Experimental results on two popular chest X-ray (CXR) datasets show that our prediction accuracy outperforms state-of-the-arts, and the learned graph adjacency matrix establishes the correlation representations of different diseases, which is consistent with expert experience. In addition, we apply an ablation study to demonstrate the effectiveness of each component in DD-GCN.