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For the chirp rate and its change rate estimation of cubic phase signal (CPS), conventional algorithms cannot achieve a trade-off between low computational cost and high performance. In this paper, by utilizing the numerical computational method (NCM), effects of Doppler frequency shift are quantified, and the relationships of the optimal signal length with the chirp rate and change rate of chirp rate are obtained. Then a fast parameter estimation algorithm (DMNUFFT), based on dechirp method (DM) and nonuniform fast Fourier transform (NUFFT), is proposed. Compared with existing algorithms, DMNUFFT can achieve high performance with relatively low computational cost. The performance analyses and an application to inverse synthetic aperture radar (ISAR) imaging are shown to validate the effectiveness of DMNUFFT.