Abstract: The tube-casing annulus generates various noises, which makes the measured coupling reflection signal very complex. The real acoustic velocity in annulus is difficult to calculate accurately. It can be calculated by Fourier transform of the original coupling data, but there are errors that cannot be ignored. The all-phase Fourier transform is an improved method of the Fourier transform to obtain a more accurate frequency spectrum and phase spectrum. In this paper, the spectrum of the original coupling signal is obtained by using the all-phase fast Fourier transform (apFFT), and then the acoustic velocity in annulus is further calculated by the spectrum. So, more accurate acoustic velocity estimation can be obtained. By using FFT and apFFT to obtain the spectrums of the simulated coupling signals under different signal-to-noise ratios (SNRs), it can be seen that apFFT has superior ability to suppress spectral leakage and better anti-noise capability than FFT. Then, according to the FFT spectrum and the apFFT spectrum, the acoustic velocity is calculated and the accuracy is compared respectively, it is verified that the acoustic velocity calculated by the apFFT spectrum is more stable and accurate. The above two methods are applied to analyzing and comparing the spectrums of the measured coupling data in different depth wells. It is shown that apFFT has better identification ability to peak positions than FFT, and so the accuracy of calculating acoustic velocity according to peak position will be higher.