The traditional beamforming method has been a common tool for extracting the trackside acoustic weak signal of axle bearing and been applied to fault diagnosis. Nevertheless, considering the severe impact interference and the strong background noise, such as the rolling noise, the effectiveness of beamforming method would be poor. In order to overcome the issue, a new successive sources deletion approach based on the kurtosis and energy estimators (noted SSD-KE) is proposed for enhancing the trackside acoustic weak signal of axle bearing. Firstly, the time-domain beamforming is performed using the acoustic signal acquired by the microphone array. Then, the strong impact interference is iteratively removed in terms of a kurtosis estimator. Likewise, the energy is employed as a subsequent statistic estimator to further remove the strong background noise. Finally, the enhanced signal could be used for the fault diagnosis. The validity of SSD-KE is first examined by numerical simulations. Different configuration parameters and noise conditions are also simulated to demonstrate the superiority and robustness of SSD-KE. Furthermore, experiments considering two different types of axle bearing faults are carried out, and the obtained results emphasize that SSD-KE has better performance on weak signal enhancement and could be used for fault diagnosis under strong background noise, even with strong impact interference.