Predicting the remaining useful life (RUL) of bearings is important for the secure running and reducing maintenance costs of rotating machinery. In this article, a novel feature extraction and RUL prediction framework of bearing is proposed by utilizing time-frequency representations (TFRs) and deep neural network with double attention (DA-DNN). Firstly, TFRs are employed to extract the degradation features associated with RUL prediction, which can effectively cope with the non-stationary properties of bearing vibration data. The reduced dimensional TFRs are then used as the DA-DNN model input. Afterwards, DA-DNN is developed by employing the double attention structure to extract the key degradation features more efficiently. The dual-attention structure has ability to capture the degradationrelated features from two aspects of channel attention and spatial attention, which enables the network to focus on high RUL-relevant information. Finally, the experimental results demonstrate the effectiveness of DA-DNN, which shows higher performance in terms of prediction accuracy compared to other deep learning (DL) methods.