Various time-frequency analysis methods have been employed for the vibration signal processing of rotating machinery under time-varying speeds. However, most methods suffer from time-frequency blurriness, particularly for signals experiencing fast changes of instantaneous frequencies. Synchroextracting Transform is a powerful post-processing tool of time-frequency analysis; its results, nevertheless, greatly depend on the original time-frequency representation. This paper proposes a matching linear chirplet based synchroextracting transform to address the problem. Chirp-rate matching strategy is firstly developed to alleviate smearing problems of time-frequency representations, where the chirp-rates adaptively match true ones of signals with the guidance of kurtosis. The matching strategy is then integrated with synchroextracting transform to further sharpen the time-frequency representation. With enhanced energy concentration level and sharpened instantaneous frequency ridges, the readability of time-frequency representation can be improved, which is also echoed by more accurate extracted instantaneous frequency ridges. Rotating machinery fault diagnosis can then be realized based on the extracted time-frequency ridges.