Abstract: A novel method based on compressed sensing (CS) is proposed to the problem of parameter estimation of linear frquency modulation (LFM) signal. Considering an LFM signal is sparse in the best fractional Fourier domain, a coarse search and a fine search is performed on the order of FrFT, and then the coefficient vectors of the LFM signal in the FrFT domain of each order is solved, finally, through threshold detection, the estimation of frequency rate and starting frequency are obtained. Under the condition of narrow-band interference, the morphological component analysis is involved in the method, which can improve the performance of the method. Experiment result shows that when the points of random projection are far less than that of Nyquist sampling, the proposed method can accurately estimate the parameter of the signal, and is insensitive to Gaussian white noise and strong narrowband interference.