Machine fault signal generally includes multiple non-stationary components with nonlinear time frequency (TF) relationship, whose wideband frequency spectrums are usually overlapped. This brings great obstacles for machine fault diagnosis. Firstly，the principle of Chirplet TF decomposition is analyzed, and an additional curvature parameter is introduced into the traditional Chirplet elementary function to match the time varying linear or non-linear components. The performance comparison between the modified version of adaptive TF representation and the other TF representation verifies that the modified version has the high TF resolution without cross-term interference and can match the non-stationary component very well. Finally, the practical fault diagnosis examples of roll bearing and gear box are given. The satisfactory results for diagnosis are acquired with the modified adaptive TF representation.