In order to solve the problem that it is difficult to accurately estimate the multipath time delay of linear frequency modulation (LFM) signals in impulse noise environment, this paper designs a new nonlinear amplitude transformation function P-NAT (piecewiseNAT) function, and proves that any random variable has finite second-order moment after transformation by this function, a multipath time delay estimation method of LFM signals based on P-NAT function is then proposed. The optimal order FRFT is performed on the transmitted signal and the noisy multipath received signal transformed by P-NAT function respectively. According to the relationship between peak position offset in FRFT domain and the time delay, the multipath time delay estimation of the LFM signal is realized. Simulation results show that this method is superior to fractional lower order statistics method and myriad filter method in impulse noise suppression, when the generalized signal-to-noise ratio is 0 dB, the normalized root mean square error of time delay estimation is less than 10 -4 . It is suitable for multipath time delay estimation of LFM signals in low signal-to-noise ratio and strong impulse noise environment.