A fast transient component extraction method of the train bearing fault acoustic signal is proposed, which is based on Doppler modulated time-shifting Laplace wavelet. It includes two steps that are rough estimation first and precise identification. The first is rough estimation of transient parameters. The existing periodic Doppler modulated Laplace wavelet model is used to roughly estimate the transient parameters. The second is precise parameter estimation and transient component extraction. A Doppler modulated time-shifting Laplace wavelet model is formulated, which uses one-by-one matching strategy to accurately estimate the transient parameters and extract the transient components. The proposed method has two advantages, which are high accuracy and high efficiency. For high accuracy, the Doppler modulation time-shifted Laplace wavelet model has only one wavelet component for positioning the delay parameter in the time domain, which can solve the matching error problem caused by the pseudo-period of the transient component. For high efficiency, because the periodic transient model is used to roughly estimate the parameters of the transient components, the range of the wavelet parameters can be set very small in the process of extracting the transient components one by one. The experiment comparison and analysis results show that the efficiency is increased by 71. 46% , compared with the direct extraction method. This study provides a method to accurately and efficiently extract transient components from train bearing fault acoustic signals containing Doppler distortion.