Based on the principle of two-beam interferometer, the demodulating theory of optical fiber Fabry-Perot sensor illuminated by Gauss distributed optical source was demonstrated via Fourier transform method. According to the characteristic of Gauss distributed optical source，the feasibility of measuring cavity length was presented by directly applying an fast Fourier transform (FFT) algorithm to the data sampled at equal optical wavelength interval and using the relation of cavity length and the peak frequency in the frequency domain. The demodulation precision was increased with frequency spectrum interpolating technology, and the experimental verification was accomplished with the help of the demodulating system constituted by broadband light source and spectrometer etc. The measured data are coincident well with theoretically calculated data.