To extract the cavity length information of optical fiber Fabry-Perot interference signal with high precision， combined with the multi-scale subdivision function of wavelet transform， the phase information of each point of the interference spectrum is accurately extracted through the wavelet ridge， and the phase compensation is carried out by using peak information， which improves the accuracy of cavity length demodulation. Simulation results show that the demodulation error of the algorithm can reach±0.06 nm in theory. The experimental results show that the cavity length demodulation resolution of the algorithm is doubled compared with that of the least square phase correction method and the resolution can reach 0.514 nm. The demodulation resolution of the acceleration sensor experiment is up to 0.9 mg. The algorithm has a certain application prospect in the high precision measurement of dynamic and static parameters of Fabry-Perot sensor.