The Fourier transform (FT) method for demodulating the extrinsic Fabry-Perot interferometer (EFPI) possesses the advantage of high resolution and wide dynamic range for the absolute measurement in demodulating white-light EFPI. However, the dynamic range and the resolution of this method are limited by the nonlinear relationship with the scanning wavelength and the fence effect of FT, respectively. The cubic spline interpolation and a modified FT algorithm are used to reduce the influence of chirped spectrum and increase the resolution, respectively. The simulation and the experimental results show that the algorithm has seventy times enhancement of the resolution of demodulation.