In order to solve the problems that the traditional bearing remaining service life (RUL) prediction method relies too much prior knowledge, the bearing degradation data is complex and the number of features is large, resulting in large prediction errors and low accuracy, a method combining principal component analysis (PCA), deep residual shrinkage network (DRSN) and time convolutional network (TCN) for predicting bearing residual life was proposed. Firstly, the extracted bearing signal features were reduced by PCA, and the features containing more degraded information were retained as new data features to reduce data complexity. Secondly, the TCN network was used to capture the temporal correlation between the life data and effectively model the bearing degradation process. Finally, through the soft threshold function and attention module of DRSN network, the interference noise in the signal was eliminated, the useful feature channel was enhanced, and the prediction accuracy was improved. XJTU data set was used to verify the validity of this method in bearing life prediction. The experimental results show that the MSE value decreased by 84.6% after PCA dimensionality reduction compared with the non-dimensionality reduction. The MAE of DRSN-TCN model was reduced by 72.7% compared with DRSN model. Compared with TCN model, MSE value decreased by 83.5%. The effectiveness of the combined method of PCA reduction and DRSN-TCN model was illustrated.