In the era of big data, high-performance rolling bearing fault diagnostic methods are of great significance to ensure manufacturing smoothly and avoid mass economic losses. A rolling bearing fault diagnostic CAR-SNN model based on Convolutional Block Attention Module (CBAM), Residual Network (ResNet), and Spiking Neural Networks (SNNs) is proposed based on deep learning (DL). The CAR-SNN model combines CBAM, ResNet, and SNNs to extract critical features while avoiding gradient vanishing or explosion phenomena. The ability of the CAR-SNN model to process spatio-temporal information is improved by using SNNs that incorporate spatio-temporal information simultaneously. The proposed model is used for the rolling bearing fault diagnosis, which datasets are from the experimental platforms of CWRU and Jiangnan University, with the highest diagnostic accuracy 99.995% and 99.18%, respectively. The experimental results validate the effectiveness and stability of the proposed model. The results of comparison experiments show that the CAR-SNN model has better fault diagnostic accuracy and stability than that of the CAR model and other comparison methods. The proposed data-driven rolling bearing fault diagnostic method based on the CAR-SNN model is easy to be implemented, and meeting the needs of high fault diagnostic accuracy in practical applications, and provides valuable input for fault diagnosis of rolling bearings.