Abstract: To attain fast and accurate estimation under low signal and noise ratio(SNR) conditions, a novel algorithm is presented. On the basis that when linear frequency modulation(LFM) signals possess the same energy and duration, their squares of spectrum amplitude are inversely proportional to their respective frequency rates, the algorithm can give estimations of initial frequency and frequency rate together only by means of searching the maximum among several groups of fast Fourier transform(FFT) maximum amplitudes. Simulation results showed that through setting proper algorithm parameters, the algorithm can be applied to LFM signals when the SNR as low as -38dB.