The output of fiber optic gyroscopes (FOG) involves Gaussian white noise and fractional noise which is difficult to eliminate by traditional methods because of the non-stationary, long-term correlation, self-similarity characteristics. On account of the characteristics of the wavelet multi-resolution analysis, wavelet analysis has become a powerful tool to study fractal noises. This paper introduces an effective technique for the de-noising of FOG corrupted by non-stationary noises. The proposed method is based on a second generation wavelet transform and level-dependent threshold estimator. The whole algorithm consists of the de-composition based on lifting wavelet, parameter estimation, and level-dependent soft threshold de-noising. The de-noising method based on traditional universal thresholding wavelet is also investigated to provide a comparison with the new method. Experimental results prove that the proposed method based on level-dependent lifting wavelet outperforms the traditional wavelet de-noising method.