In this paper, a bearing fault diagnosis method based on local maximum peaks of cepstrum is proposed. At first, the cepstrum of original signal is calculated. An index named local maximum peak is proposed to extract fault features. Then the binary tree classification method is adopted to complete the feature classification process by setting multiple thresholds or blind areas. The method based on the local maximum peak and its distribution domain is used to determine the threshold. After feature classification, each condition is limited by several limited conditions to complete fault diagnosis. In order to verify the accuracy of the proposed method, test data from practical bearing fault experiments are used in simulation experiments. The results show that the accuracy of the proposed method reached 98.44% and the running time was only 2.1810s, which proved the accuracy and effectiveness. The method has higher accuracy and less running time compared with original cepstrum and other spectral analysis techniques. This approach provides a new idea for fault diagnosis of rolling bearing under condition of constant speed.