Recent advances in long short-term memory (LSTM) networks have enabled us to handle sequential and time-series data. However, some applications of LSTM networks in the healthcare domain have produced suboptimal performances, as the algorithm assumes constant elapsed times between consecutive elements of a patient health record. In reality, patient health records are heterogeneous information with irregular time intervals and different sequence lengths. The heterogeneity and temporal dynamics of the patients’ data make it challenging to analyze long-timescale progression patterns of disease when we use traditional LSTM networks. This study proposes a novel LSTM architecture, called Time-Aware LSTM with power-law decay (T-pLSTM) networks, which can capture time irregularity and long-term dependency of patients’ data. T-pLSTM can handle long-timescale patient records with irregular elapsed time by power-law forget gate and adjusted memory cell. The proposed model was tested to predict tumor size and survival month over time for non-small cell lung cancer (NSCLC) patients. The model was trained on patient records obtained from the Surveillance, Epidemiology, and End Results (SEER) Research Plus database, and its performance was evaluated by comparative analysis. The experiments using datasets with fixed and different sequence lengths showed that T-pLSTM outperformed the standard LSTM models. This result implies improvement of learning for long-term scale information with time irregularity in LSTM networks.