The chirp rate estimation algorithm of the linear frequency modulation is studied. But the linear frequency modulation of the space-borne SAR azimuth signals, which is generated by the Doppler Effect. Its chirp rate is very small. The normal estimation algorithm of the chirp rate for single pulse will be failure. The local wave decomposition is put forward in this article. Through the LWD analyzing, and then estimating the chirp rate of the burst, the azimuth chirp rate estimation can be realized. The simulation experiment proves its rationality.