This paper generalizes the Fractional Fourier transform (FRFT) to estimate the parameters of the Quadratic frequency modulated (QFM) signal. Firstly, the proposed algorithm transforms the QFM signal into the Linear frequency modulated (LFM) signal by means of the instantaneous autocorrelation function, and then the parameter estimation of the QFM signal is performed by the FRFT and dechirping method. In order to calculate discrete sampling values of the FRFT, an adaptive FRFT algorithm based on the Least mean square (LMS) is proposed. Extension to the multicomponent and higher order frequency modulated signals is also discussed. Finally, the effects of delay parameter on estimation performances are investigated through Monte Carlo simulations and the results of simulations verify the effectiveness of the proposed algorithm.