To improve the real-time performance of distributed optical fiber sensing system based on Brillouin scattering, through the analysis of the strengths and weaknesses of the classical Lorentzian and pseudo-Voigt models fitting methods, the multi-layer feedforward artificial neural network (ANN) method was used to estimate the Brillouin frequency shift. The structure, input and output, activation function, and training algorithm of the ANN were determined. The ANN was trained by simulated Brillouin spectra with different signal-to-noise ratios (5dB~40dB) and Brillouin frequency shifts (10.62GHz~10.82GHz). The Brillouin frequency shift estimation error of the trained ANN for the training samples was only about 1MHz. At the same time, the radial basis function ANN was also trained. For the Brillouin spectra with temperature and strain varied along the optical fiber, the trained multi-layer feedforward ANN and radial basis function ANN, the spectrum fitting methods based on the Lorentzian model and the pseudo-Voigt model were respectively used to estimate the Brillouin frequency shift along the optical fiber, and at the same time the temperature and strain along the optical fiber were obtained by demodulation. The results show that the accuracy of the multi-layer feedforward ANN method is similar to that of the classical spectral fitting method based on the Lorentzian and pseudo-Voigt models, but the calculation time is only 1/947.16~1/470.95 and 1/784.56~1/532.88 of the latter two. This work provides a reference for the rapid measurement of optical fiber temperature and strain based on Brillouin scattering.