For targets with complex motions, the time-varying Doppler frequency deteriorates inverse synthetic aperture radar (ISAR) images. After range alignment and phase adjustment, azimuth echoes in a range cell can be modeled as multicomponent cubic phase signals (CPSs). The chirp rate and the quadratic chirp rate of the CPS are identified as the causes of the time-varying Doppler frequency; thus, it is necessary to estimate these two parameters correctly to obtain a well-focused ISAR image. The parameter-estimation algorithm based on the modified chirp rate-quadratic chirp rate distribution (M-CRQCRD) is proposed for the CPS and applied to the ISAR imaging of targets with complex motions. The computational cost of M-CRQCRD is low, because it can be implemented by the fast Fourier transform (FFT) and the nonuniform FFT easily. Compared to two representative parameter-estimation algorithms, the M-CRQCRD can acquire a higher antinoise performance due to the introduction of an optimal lag-time. Through simulations and analyses for the synthetic radar data, the effectiveness of the M-CRQCRD and the imaging algorithm based on the M-CRQCRD are verified.