The problem of "mode mixing" is one of the main problems limiting the empirical mode decomposition in engineering applications. An improved algorithm of complementary ensemble empirical mode decomposition (CEEMD) as empirical mode decomposition (EMD) improves the mode mixing problem of EMD to some extent. However, the standard CEEMD method still empirically set the amplitude of white noise, and it is not adaptive to deal with the mode mixing problem. By studying the phenomenon of modal aliasing, its essence is that the intrinsic mode function (IMF) is obtained by decomposing the signal generates certain information coupling phenomenon, which cannot make the IMF component accurately reflect the real components of the signal. Therefore, this paper proposes to embed grid search algorithm (GSA) in the process of decomposing signals with CEEMD, and to construct an adaptive CEEMD method by taking least squares mutual information (LSMI) as the fitness function of GSA. The algorithm adaptively searches for the optimal white noise amplitude, corrects a small number of coupling frequency components generated during signal decomposition, ensures the orthogonality of information between each IMF component, and further inhibits the mode aliasing problem. Finally, the effectiveness of the proposed method is verified by simulation test, and it is used to extract the characteristic frequency of micro-fault of rolling bearing. The experimental results show that the algorithm has less iteration numbers, less IMF components and relatively less calculation amounts in the application of micro-fault feature extraction of rolling bearing.