First, it is pointed out that the widely used Fast-Dechirp algorithm can't be applied to low CNR LFM signals for the reason of SNR-loss existing during self-correlation operation. To attain accurate estimation under extremely-low-CNR condition, a novel algorithm is presented. It bases on the fact that when LFM signals have the same energy and duration their square of spectrum amplitudes are inverse proportional to frequency rates. Merely by means of searching the largest one among several groups of FFT maximum amplitudes, it can give out estimations of initial frequency and frequency rate together, thus easy to be implemented. Simulation results show that through setting proper algorithm parameters, the algorithm can be applied to much lower CNR conditions(available at 20dBHz) than the Fast-Dechip algorithm.