Stochastic noises of fiber optic gyroscope (FOG) mainly contain white noise and fractal noise whose long-term dependent component causes FOG a rather slow drift. In order to eliminate this component, a two-step filtering methodology is proposed. Firstly, fractional differencing (FD) method is introduced to trans-form fractal noise into fractional white noise based on the estima-tion of Hurst exponent for long-term dependent fractal process, which together with the existing white noise make up of a gener-alized white noise. Further, an improved denoising algorithm of wavelet maxima is developed to suppress the generalized white noise. Experimental results show that the basic noise terms of FOG greatly decrease, and especially the slow drift is restrained effectively. The proposed methodology provides a promising ap-proach for filtering long-term dependent fractal noise. Stochastic noises of fiber optic gyroscope (FOG) mainly contain white noise and fractal differencies whose long-term dependent component causes FOG a rather slow drift. FD) method is introduced to trans-form fractal noise into fractional white noise based on the estima-tion of Hurst exponent for long-term dependent fractal process, which together with the existing white noise make up of a gener-alized white noise. , an improved denoising algorithm of wavelet maxima is developed to suppress the generalized white noise. Experimental proposed show that the basic noise terms of FOG greatly decrease, and especially the slow drift is restrained effectively. long-term dependent fractal noise.