With the rapidly growing volume and variety of Electronic Health Records (EHR) data, deep-learning models exhibit state-of-the-art performance for many predictive tasks in the health domain. To overcome the challenge of high dimensionality in EHR data, many representation learning methods have been proposed to learn low-dimensional diagnosis representations. Another challenge is how to effectively incorporate the domain knowledge, such as the International Classification of Diseases (ICD) medical ontology, into the learned embeddings. Albeit the medical ontology is a knowledge graph, none of the existing methods take advantage of Graph Neural Network (GNN), which has demonstrated its ability in other domains. The problem is that a GNN with multiple hidden layers, which are required to propagate information from the leaf of the medical ontology graph to the root, dilutes the differences among the nodes, degrading the quality of the learned embeddings. In this paper we introduce a densely connected graph derived from the original ontology graph to tackle the problem. Furthermore, to model the information in patient records, we construct a single co-occurrence graph based on the co-occurrence of diagnoses and a patient’s diagnosis history. Experimental results show that the diagnosis embeddings learned from our model, DUal-GRAph Representation Learning (DUGRA), outperform the current state-of-the-art models in terms of diagnosis prediction accuracy.