The phase error presents for sample error and dispersion of the fiber in optical fiber Fourier transform spectrometer(FFTS),distortion of spectrum can be induced. Multiplicative method can correct phase error in frequency domain. The calculated low-resolution phase spectrum with short two-sided interferogram corrects the high-resolution spectrum through high resolution amplitude spectrum multiplied by the cosine of the difference of low resolution and high resolution phase spectrum by using multiplicative procedure which is operated in frequency domain. The results show that multiplicative method is also effective in FFTS. Phase corrected spectrum agrees well with spectrum from commercial grating spectrum instrument. The method,which is not only simpler and faster than the others,but also has high resolution,and remains the features of noise and keeps the baseline immune to noise,can be widely applied in FFTS.