Abstract: A quadratic estimation algorithm is proposed to reduce the complexity of accurate Linear Frequency Modulation (LFM) parameter estimation. First, the frequency rate and initial frequency are estimated coarsely by short time coherent integral and incoherent accumulation. Then, the parallel Partial Matched Filters combined with FFT (PMF-FFT) and quadratic interpolation are utilized to estimate the residuals of the frequency rate and initial frequency. Last, the final estimated values are obtained by synthesizing the results of both estimations. Simulation shows that the proposed algorithm has a low SNR threshold, and the accuracy is close to Cramer-Rao Lower Bound (CRLB). The complexity and hardware consumption of the proposed algorithm are much less than the frequency rate test algorithm and joint estimation algorithm based on interpolation.