To solve the problem of high output noise and low output precision of gyroscope in micro-electromechanical systems(MEMS). Based on the adaptive filtering algorithm and the wavelet threshold algorithm, the wavelet threshold algorithm and the fuzzy theory are combined，this paper proposed to apply the Sage-Husa adaptive filtering algorithm combined with the wavelet fuzzy threshold denoising algorithm to MEMS gyroscope denoising. Firstly, the improved Sage-Husa adaptive filtering algorithm is used to preprocess, and the influence of interference data on filtering is suppressed by modifying the predicted value of the state. Then, the wavelet fuzzy threshold denoising algorithm is used to post-process the signal, so as to achieve the effect of suppressing random noise. The experimental results show that the denoising effect of the algorithm is better than the Sage-Husa adaptive filtering algorithm and the wavelet threshold algorithm, the noise variance is reduced by 78.4% and 14.6%, and the signal-to-noise ratio is increased by 43.7% and 16.3% respectively in the static experiment. The algorithm can adaptively reduce the adverse effects of outliers and maintain the original signal waveform. Compared with Sage-Husa adaptive filtering algorithm and wavelet fuzzy threshold algorithm, the noise variance is reduced by 62.7% and 31.6%, and the signal-to-noise ratio is increased by 47.8% and 10.0% respectively in dynamic experiments.