Aiming at the problem of energy leakage that occurs during the course of phase-extraction by using conventional fast Fourier transform (FFT) algorithm, an novel method that acquisition interferogram is firstly tailored to a few full-period of fringes is proposed to suppress the influence of energy leakage on the precision of phase-extraction. The precision of fast Fourier transform phase-extraction algorithm can be efficiently improved by tailoring the interferogram. Furthermore, a new subdivision method, which is based on the time-shift property of fast Fourier transform, for moiré interference fringes is developed. Compared with conventional fast Fourier transform phase-extraction algorithm, this new method pioneers a larruping means for fringes subdivision and can achieve high precision. It needs only to run fast Fourier transform algorithm twice to obtain the phase-shift between two sequential interferograms. The corresponding calculating time can then be greatly saved because it does not need to intersect the fundamental frequency of interferogram from spectral domain and inversely transform it into time domain again. Numerical results show that subdivision precision can reach 10-12 level for ideal situation that the interferogram is formed by two coherent plane waves and can be tailored to a few full-period of fringes. It can reach 10-3 level when the inteferogram is formed by two Gaussian waves.