The precise estimate of remaining useful life (RUL) is vital for the prognostic analysis and predictive maintenance that can significantly reduce failure rate and maintenance costs. The degradation-related features extracted from the sensor streaming data with neural networks can dramatically improve the accuracy of the RUL prediction. The Temporal deep degradation network (TDDN) model is proposed to make the RUL prediction with the degradation-related features given by the one-dimensional convolutional neural network (1D CNN) feature extraction and attention mechanism. 1D CNN is used to extract the temporal features from the streaming sensor data. Temporal features have monotonic degradation trends from the fluctuating raw sensor streaming data. Attention mechanism can improve the RUL prediction performance by capturing the fault characteristics and the degradation development with the attention weights. The performance of the TDDN model is evaluated on the public C-MAPSS dataset and compared with the existing methods. The results show that the TDDN model can achieve the best RUL prediction accuracy in complex conditions compared to current machine learning models. The degradation-related features extracted from the high-dimension sensor streaming data demonstrate the clear degradation trajectories and degradation stages that enable TDDN to predict the turbofan-engine RUL accurately and efficiently.