Remaining Useful Life (RUL) prediction is significant in indicating the health status of the sophisticated equipment, and it requires historical data because of its complexity. The number and complexity of such environmental parameters as vibration and temperature can cause non-linear states of data, making prediction tremendously difficult. Conventional machine learning models such as support vector machine (SVM), random forest, and back propagation neural network (BPNN), however, have limited capacity to predict accurately. In this paper, a two-phase deep-learning-model attention-convolutional forget-gate recurrent network (AM-ConvFGRNET) for RUL prediction is proposed. The first phase, forget-gate convolutional recurrent network (ConvFGRNET) is proposed based on a one-dimensional analog long short-term memory (LSTM), which removes all the gates except the forget gate and uses chrono-initialized biases. The second phase is the attention mechanism, which ensures the model to extract more specific features for generating an output, compensating the drawbacks of the FGRNET that it is a black box model and improving the interpretability. The performance and effectiveness of AM-ConvFGRNET for RUL prediction is validated by comparing it with other machine learning methods and deep learning methods on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset and a dataset of ball screw experiment.