In remaining useful life(RUL) prediction methods for bearings based on deep learning, temporal convolutional networks(TCNs) does not consider the future time information of vibration data, long and short-term memory(LSTM) networks are difficult to learn long time series data features effectively. To solve the above problems, a bearing RUL prediction method based on the parallel bidirectional temporal convolutional network and bidirectional long and short-term memory network is proposed. First, the multi-sensor data are normalized, and the data of each sensor are merged by channel to achieve efficient fusion of multi-sensor data. Then, a parallel dual network structure is constructed by using the Bi-TCN and Bi-LSTM, in which the Bi-TCN goes to learn the bi-directional long time series features and the Bi-LSTM goes to learn the time-dependent features, so the parallel dual network structure can learn richer vibration signal features. Meanwhile, a feature fusion attention mechanism is developed to fuse the output features of the dual network structure, which calculates the output weights of the Bi-TCN and Bi-LSTM to achieve adaptive weighted fusion of the output features. Finally, the fused features are passed through the fully connected layer to output the prediction results of the bearing RUL. RUL prediction experiments are conducted using Xián Jiaotong University bearing dataset and PHM 2012 bearing dataset respectively. The results show that, compared with the advanced prediction methods, the proposed method can accurately predict the RUL of more types of bearings and has lower prediction errors.