The time-frequency analysis methods are used to study the time-frequency distribution characteristics of non-stationary signal with noise. De-shape SST (De-shape synchrosqueezing transform) algorithm has good time-frequency performance. However, the anti-noise performance and robustness of the algorithm still need to be improved. A De-shape SST algorithm based on nonlinear matching pursuit decomposition (NDSST) is proposed. The sparse reconstruction of non-stationary signals is carried out via the excellent reconstruction feature of NMP, and then the time-frequency analysis by De-shape SST is performed. The approach in this article can improve the capability of noise reduction and robustness of the algorithm. Meanwhile, an accurate time-frequency aggregation is retained. The numerical simulation results show that the NDSST algorithm can obtain the time-frequency representation with high concentration for single frequency, variable frequency, linear frequency modulation and combined frequency conversion signal. And it has excellent anti-noise property in the low signal noise ratio (SNR) conditions. In the analysis and applications of metal rupture signal, the NDSST algorithm can clearly get the time and instantaneous frequency range of metal rupture. It provides a threshold value for setting up monitoring transducer in engineering practice.