To overcome the disadvantage of low demodulation accuracy of reflective spectrum of fiber Bragg grating sampled by portable demodulator, a wavelet transform-based Gaussian(WTG) curve fitting method is introduced. The reflection spectrum signal is decomposed by wavelet transform, and the wavelet detail component is quantized by threshold. On this basis, the signal is reconstructed by the processed detail component and approximate component. Then, the reconstructed signal is interpolated to fit the Gauss curve, and the Levenberg-Marquardt(LM) algorithm is used to optimize the Gauss fitting coefficient. The simulation results show that the WTG algorithm has the smallest peak positioning error and higher demodulation accuracy compared with the direct peak seeking algorithm and the Gauss fitting algorithm.