Fourier transform white-light interferometry possesses high resolution and wide dynamic range for the absolute measurement of fiber optic interferometric sensors. However, the white-light optical spectrum distributed along wavelength is a chirp signal because the phase of the optical spectrum has a nonlinear relationship with the scanning wavelength. The chirped spectrum is considered as a constant period signal when it is Fourier transformed. The chirp in the period would bring errors into the phase shift and reduce the measurement resolution. A nonlinear wavelength sampling algorithm is proposed in this paper. The chirp characteristics of the white-light optical spectrum are considered, and the nonlinear wavelength sampling intervals vary with the wavelength. By using the nonlinear wavelength sampling algorithm, the errors in the phase shift can be reduced effectively, whereas the chirp characteristics of the signals can be retained entirely for filtering and extracting the chirped optical spectrum signals from the composite signal. The experimental results show that the standard deviation decreases from 0.016 to 0.005 μm by using the nonlinear wavelength sampling, when a fiber optic extrinsic Fabry-Perot interferometric sensor with a cavity length of 1512.2 μm is interrogated.