In order to detect the incipient fault of rolling bearings and to effectively identify fault characteristics, based on amplitude-aware permutation entropy (AAPE), an enhanced method named hierarchical amplitude-aware permutation entropy (HAAPE) is proposed in this paper to solve complex time series in a new dynamic change analysis. Firstly, hierarchical analysis and AAPE are combined to excavate multilevel fault information, both low-frequency and high-frequency components of the abnormal bearing vibration signal. Secondly, from the experimental analysis, it is found that HAAPE is sensitive to the early failure of rolling bearings, which makes it suitable to evaluate the performance degradation of a bearing in its run-to-failure life cycle. Finally, a fault feature selection strategy based on HAAPE is put forward to select the bearing fault characteristics after the application of the least common multiple in singular value decomposition (LCM-SVD) method to the fault vibration signal. Moreover, several other entropy-based methods are also introduced for a comparative analysis of the experimental data, and the results demonstrate that HAAPE can extract fault features more effectively and with a higher accuracy.