A convolutional neural network (CNN) has been used to successfully realize end-to-end bearing fault diagnosis due to its powerful feature extraction ability. However, the CNN is prone to focus on local information, ignoring the relationship between the whole and the part of the signal due to its unique structure. In addition, it extracts some fault features with poor robustness under noisy environment. A novel diagnosis model based on feature fusion and feature selection, GL-mRMR-SVM, is proposed to address this problem in this paper. First, the model combines the global features in the time-domain and frequency-domain of the raw data with the local features extracted by CNN to make full use of the signal information and overcome the weakness of traditional CNNs neglecting the overall signal. Then, the max-relevance min-redundancy (mRMR) algorithm is used to automatically extract the discriminative features from the fused features without any prior knowledge. Finally, the extracted discriminative features are input into the SVM for training and output the fault recognition results. The proposed GL-mRMR-SVM model was evaluated through experiments on bearing data of Case Western Reserve University (CWRU) and CUT-2 platform. The experimental results show that the proposed method is more effective than other intelligent diagnosis methods.