The Intensive Care Unit (ICU) is one of the most important parts of a hospital, which admits critically ill patients and provides continuous monitoring and treatment. Various patient outcome prediction methods have been attempted to assist healthcare professionals in clinical decision-making. Existing methods focus on measuring the similarity between patients using deep neural networks to capture the hidden feature structures. However, the higher-order relationships are ignored, such as patient characteristics (e.g., diagnosis codes) and their causal effects on downstream clinical predictions. In this paper, we propose a novel Hypergraph Convolutional Network that allows the representation of non-pairwise relationships among diagnosis codes in a hypergraph to capture the hidden feature structures so that fine-grained patient similarity can be calculated for personalized mortality risk prediction. Evaluation using a publicly available eICU Collaborative Research Database indicates that our method achieves superior performance over the state-of-the-art models on mortality risk prediction. Moreover, the results of several case studies demonstrated the effectiveness of constructing graph networks in providing good transparency and robustness in decision-making.