The remaining useful life (RUL) prediction of rolling bearings based on vibration signals has attracted widespread attention. It is not satisfactory to adopt information theory (such as information entropy) to realize RUL prediction for complex vibration signals. Recent research has used more deep learning methods based on the automatic extraction of feature information to replace traditional methods (such as information theory or signal processing) to obtain higher prediction accuracy. Convolutional neural networks (CNNs) based on multi-scale information extraction have demonstrated promising effectiveness. However, the existing multi-scale methods significantly increase the number of model parameters and lack efficient learning mechanisms to distinguish the importance of different scale information. To deal with the issue, the authors of this paper developed a novel feature reuse multi-scale attention residual network (FRMARNet) for the RUL prediction of rolling bearings. Firstly, a cross-channel maximum pooling layer was designed to automatically select the more important information. Secondly, a lightweight feature reuse multi-scale attention unit was developed to extract the multi-scale degradation information in the vibration signals and recalibrate the multi-scale information. Then, end-to-end mapping between the vibration signal and the RUL was established. Finally, extensive experiments were used to demonstrate that the proposed FRMARNet model can improve prediction accuracy while reducing the number of model parameters, and it outperformed other state-of-the-art methods.