The Levenberg-Marquardt (LMA) is used for the demodulation of absolute Fabry-Pérot (F-P) cavity based on the optical fiber white-light interferometry that is more efficient than cross correlation algorithm. High immunity to the perturbation of the source power is achieved by its Gauss-fitting and setting limitation to the parameters of LMA. Signal data selection principle is discussed and standard deviations of experimental device and LMA under the perturbation of power are measured.