Rotating machinery usually works in the time-varying speed condition so that the vibration signal which contains rich health information also shows strong non-stationarities. Constrained by limited time-frequency（TF）resolution，the ideal time-frequency representation（TFR）cannot be obtained when the frequency of the analyzed signal varies. Based on the fact that a single linear chirplet transform can improve the concentration level of the TFR when the slope of the frequency is consistent with the chosen chirp ?rate in LCT，a new time-frequency analysis（TFA）method is proposed，named as adaptively matching chirp-rate linear transform（AMCLT）. To better match the changing frequency of the signal，chirprate determination strategy guided by kurtosis is proposed. To simplify the algorithm，the original linear transform kernel is advanced to make the proposed method increase the TFR concentration level when analyzing multiple frequency-modulated signals without iterations. Besides，the proposed method also allows for the perfect signal reconstruction of the interested frequency components. The analyzing results of vibration signal shows that，in terms of readability of the TFR，the proposed method can acquire the improved TFR with more concentrated energy and free from cross term interference. In terms of the feature extraction，the proposed method can extract the fault related features in the rotating machinery vibration signal more accurately and can be effectively applied to fault diagnosis of rotating machinery.