The vibration signals collected by acceleration sensors are interspersed with noise interference, which increases the difficulty of fault diagnosis for rolling bearings. For this reason, a rolling bearing fault diagnosis method based on complete ensemble empirical model decomposition with adaptive noise (CEEMDAN) and improved convolutional neural network (CNN) is proposed. Firstly, the original vibration signal is decomposed into a series of intrinsic modal function (IMF) components using the CEEMDAN algorithm, the components are filtered according to the correlation coefficients and the signals are reconstructed. Secondly, the reconstructed signals are converted into a two-dimensional grey-scale map and input into a convolutional neural network to extract the features. Lastly, the features are inputted into a support vector machine (SVM) with the optimised parameters of the grey wolf optimiser (GWO) to perform the identification and classification. The experimental results show that the rolling bearing fault diagnosis method based on CEEMDAN and CNN-SVM proposed in this paper can significantly reduce the noise interference, and its average fault diagnosis accuracy is as high as 99.25%. Therefore, it is feasible to apply it in the field of rolling bearing fault diagnosis.