A new method for estimating parameters of quadratic frequency modulated signals is proposed basing on a product kernel function. Firstly, the signal is multiplied by its conjugate reverse signal with the phase-matching transformation being performed, and then the estimated value of the chirp rate can be obtained by searching one-dimension maximum position of accumulated signals. Secondly, the chirp rate of the signal is compensated and a new product kernel function for the dechirped signal is structured to transform it into the two-dimensional time-lag domain, and the phase-matching transformation and FFT respectively are performed along time and lag axis. As a result, by the maximum searching in the new change rate of the chirp rate-frequency domain after transformation, the estimated values of both the change rate of the chirp rate and the center frequency can be obtained, with the phase of the signal being able to compensated and the amplitude estimated by calculating the magnitude of its average, thereby leading to the reconstruction of the signal. It is shown that the proposed method precludes the iterative search of all phase parameters and improves the operational efficiency. Finally, the paper presents the simulated results that confirm the effectiveness of this method.