In this paper, a novel time-frequency (TF) analysis (TFA) method is proposed for observing vibration fault signals in rotating machinery. Our proposed method is termed the wavelet-based transient-extracting transform (WTET), which introduces a group delay (GD) estimated along the time direction to construct a reassignment operator. The operator is used to extract the coefficients on the TF ridge where most of the energy in the original wavelet transform is concentrated. As a post-processing process of wavelet transform (WT), it can improve the influence of Heisenberg uncertainty principle and enhance the prominent feature of WT in the TF plane, so as to realize the precise localization of TF distribution of the transient characteristics of signal. Compared with the reassignment method (RM), the proposed method not only improves the TF readability, but also maintains the ability to approximately reconstruct the signal. Because the proposed method only extracts the values of the GD trajectory, it has better noise robustness than the synchrosqueezing transform. Two quantitative indexes (Rényi entropy and kurtosis) are introduced to evaluate the performance between the proposed method and other improved time-frequency analysis methods. The effectiveness of the proposed method is proved by the introduction of numerical signal and real signal.