The distributed optical fiber sensor based on Rayleigh spectral demodulation has the advantages of high linearity and capability for both dynamic and static signal sensing, but the traditional demodulation method based on cross-correlation requires a large amount of calculation. Here we propose a new demodulation method based on an artificial neural network (ANN) instead of cross-correlation operation to boost the speed in the demodulation of Rayleigh backscattering spectra, in which an ANN model is first constructed and trained to map the Rayleigh scattering pattern to the frequency of the corresponding probe laser. Then, the strain or temperature information of the fiber is figured out from the input Rayleigh scattering curve to be demodulated. In the verification experiment, the Rayleigh backscattering traces at the detection position under different probe laser frequencies are obtained using time-gated digital optical frequency domain reflectometry in which chirped pulses and matched filters are employed. It is verified that the strain applied to the fiber can be correctly demodulated by the data-treatment method based on the ANN algorithm. Compared with the demodulation method based on cross-correlation, the proposed method possesses a lower signal-noise ratio and the calculation speed increased by two orders, which ensures the realization of the fast detection of dynamic signals.