A demodulation algorithm based on all-phase filters was proposed for fiber Bragg grating noise reduction. The all-phase filter can configure the filter coefficients rapidly and flexibly according to the frequency characteristics of the fiber Bragg grating signal, which can effectively filter out the high-frequency components mixed in the original signal by controlling the filter boundary adaptively. The analytical expression of the filter was deduced, and the amplitude-frequency characteristics of the filter was analyzed with the digital frequency characteristics of fiber Bragg grating signals. The experimental results show that the proposed filtering algorithm has an adaptive performance in processing fiber Bragg grating signals at different sampling intervals. This algorithm has a similar wavelength stability compared with the Gaussian fitting method, but the average demodulation time is shortened by 10 times. The wavelength demodulation stability is improved by 30% compared with the centroid method.