In order to suppress the random shift error of laser gyro and improve the practical precision of inertial navigation system, an improved gyro filtering method is proposed by combining the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and principal component analysis (PCA). Firstly, the gyro signal is decomposed by CEEMDAN, and the noise energy of each intrinsic mode function (IMF) is estimated according to the distribution model of noise energy. Then, on basis of noise energy, the principal component analysis is used to remove the noise IMF to achieve the final denoising of gyro signal. In the proposed method, CEEMD can improve the mode mixing and denoising effect of gyro signal. Moreover, PCA is used to decompose each IMF. According to the noise energy, the noise of each IMF is removed adaptively to avoid the selection of noise IMF and better retain the useful information of the signal. The proposed method is completely dependent on the characteristics of gyro signal and has good adaptability and strong denoising ability. Furthermore, the filtered effect of different methods is analyzed by overlapping Allan variance. The experimental results show that the proposed method can suppress the gyro random drift more efficiently, and the effect of removing noise is better than EMD threshold method and EMD correlation coefficient method.