The applications of Micro-Electro-Mechanical-System (MEMS) gyros in inertial navigation system is gradually increasing. However, the random drift of gyro deteriorates the system performance which restricting the applications of high precision. We propose a bias drift compensation model based on two-fold Interpolated Complementary Ensemble Local Mean Decomposition (ICELMD) and autoregressive moving average-Kalman filtering (ARMA-KF). We modify CELMD into ICELMD, which is less complicated and overcomes the endpoint effect. Further, the ICELMD is combined with ARMA-KF to separate and simplify the preprocessed signal, resulting improved denoising performance. In the model, the abnormal noise is removed in preprocess by 2σ criterion with ICELMD. Then, continuous mean square error (CMSE) and Permutation Entropy (PE) are both applied to categorize the preprocessed signal into noise, mixed and useful components. After abandon the noise components and denoise the mixed components by ARMA-KF, we rebuild the noise suppression signal of MEMS gyro. Experiments are carried out to validate the proposed algorithm. The angle random walk of gyro decreases from 2.4156∘/h to 0.0487∘/h, the zero bias instability lowered from 0.3753∘/h to 0.0509∘/h. Further, the standard deviation and the variance are greatly reduced, indicating that the proposed method has better suppression effect, stability and adaptability.