A new denoising algorithm is proposed aiming to decrease the random error of MEMS gyroscope. Firstly, the original data is decomposed into multiple intrinsic mode functions ( IMFs) using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Then the IMFs are divided into noise IMF, mixed IMF, and signal IMF according to multi-scale permutation entropy with Mahalanobis distance. Next, the noise IMF is denoised by wavelet packet (WP) and the mixed IMF is denoised by Savitzky-Golay filter (SG). Finally, the denoised signal is obtained via reconstructing the processed IMF and the signal IMF. The bumps signal is increased from 6 dB to 17 dB, and the mean square error is reduced by 71. 9% after denoising through the proposed method. The angular random walk of the denoised signal is reduced by 31. 5% in the experimental analysis of the measured gyroscope static data, which illustrates that the proposed method can predominantly improve the accuracy of MEMS gyroscope accuracy.