Modeling patient disease progression using Electronic Health Records (EHRs) is critical to assist clinical decision making. Long-Short Term Memory (LSTM) is an effective model to handle sequential data, such as EHRs, but it encounters two major limitations when applied to EHRs: it is unable to interpret the prediction results and it ignores the irregular time intervals between consecutive events. To tackle these limitations, we propose an attention-based time-aware LSTM Networks (ATTAIN), to improve the interpretability of LSTM and to identify the critical previous events for current diagnosis by modeling the inherent time irregularity. We validate ATTAIN on modeling the progression of an extremely challenging disease, septic shock, by using real-world EHRs. Our results demonstrate that the proposed framework outperforms the state-of-the-art models such as RETAIN and T-LSTM. Also, the generated interpretative time-aware attention weights shed some lights on the progression behaviors of septic shock.