Intelligent fault diagnosis algorithm for rolling bearings has received increasing attention. However, in actual industrial environments, most rolling bearings work under severe working conditions of variable speed and strong noise, which makes the performance of many intelligent fault diagnosis methods deteriorate sharply. In this regard, this paper proposes a new intelligent diagnosis algorithm for rolling bearing faults based on a residual dilated pyramid network and full convolutional denoising autoencoder (RDPN-FCDAE). First, a continuous wavelet transform (CWT) is used to convert original vibration signals into time-frequency images. Secondly, a deep two-stage RDPN-FCDAE model is constructed, which is divided into three parts: encoding network, decoding network and classification network. In order to obtain efficient expression of data denoising feature of encoding network, time-frequency images are first input into the encoding-decoding network for unsupervised pre-training. Then pre-trained coding network and classification network are combined into residual dilated pyramid full convolutional network (RDPFCN) for parameter fine-tuning and testing. The proposed method is applied to bearing vibration datasets of test rig with different speeds and noise modes. Compared with representative machine learning and deep learning method, the results show that the algorithm proposed is superior to other methods in diagnostic accuracy, noise robustness and feature segmentation ability.