A novel data processing method for demodulating the information from the interference spectrum of a white light extrinsic Fabry-Prot interferometer (EFPI) sensor system is presented. In the white light EFPI sensor system, an 850 nm LED is used as the broadband light source and a HR2000 high resolution miniature spectrometer is used to measure the interference spectrum. Through tracing a special peak point in the interference spectrum, the air gap value of the EFPI sensor can be demodulated. The order ambiguity problem of single peak tracing method is solved through the application of BP neural networks. As the BP neural networks can distinguish the interference orders of the peaks in the interference spectrum, many peaks can be traced continuously. Both high precision and large dynamic range are achieved. The data processing method is demonstrated on a white light EFPI strain sensor system. 0.1 με precision and 500 με measurement range are achieved with this system.