A new bearing intelligent fault diagnosis method was proposed, aiming at the problems of limited feature extraction and inaccurate fault detection in traditional fault diagnosis methods. A continuous wavelet convolutional layer was constructed to replace the initial convolutional layer in the convolutional neural network (CNN) for extracting the primary features of the bearing data. The enhanced ACON activation function was used to process the extracted vibration signals. A new computational space was designed to improve the overall adaptivity of CNN. Comparative experiments of rolling bearing fault diagnosis methods based on the Case Western Reserve University bearing dataset were carried out. Experimental results showed that the fault diagnosis accuracy of the proposed method was improved by 7.45, 4.46 and 1.53 percentage points, respectively, and the convergence speed of CNN was faster compared with the traditional fault diagnosis methods based on CNN, the fast Fourier transform with CNN, the long short-term memory with CNN. In the generalization task for different working conditions, the proposed method had an average accuracy of 99.64%, demonstrating superior accuracy and generalisability.