Deep learning has demonstrated success in health risk prediction especially for patients with chronic and progressing conditions. Most existing works focus on learning disease patterns from longitudinal patient data, but pay little attention to the disease progression stage itself. To fill the gap, we propose a Stage-aware neural Network (StageNet) model to extract disease stage information from patient data and integrate it into risk prediction. StageNet is enabled by (1) a stage-aware long short-term memory (LSTM) module that extracts health stage variations unsupervisedly; (2) a stage-adaptive convolutional module that incorporates stage-related progression patterns into risk prediction.We evaluate StageNet on two real-world datasets and show that StageNet outperforms state-of-the-art models in risk prediction task and patient subtyping task. Compared to the best baseline model, StageNet achieves up to 12% higher AUPRC for risk prediction task on two real-world patient datasets. StageNet also achieves over 58% higher Calinski-Harabasz score (a cluster quality metric) for a patient subtyping task.