Aiming at the problem that bearing composite fault features are difficult to be separated and extracted under strong background noise, a new compound faults diagnosis method is proposed in this paper based on fast independent component analysis ( FastICA), beetle antennae search algorithm ( BAS) and maximum correlated kurtosis deconvolution ( MCKD). Firstly, FastICA method is introduced for blind separation of rolling bearing multi-channel fault signals. Secondly, the deconvolution period T, filter length L and shift number M of the deconvolution algorithm for MCKD are simultaneously optimized by using BAS. Then an adaptive analysis method based on BAS-MCKD for vibration signal of rolling bearing is constructed to achieve noise reduction and feature enhancement of separated signals. Finally, the Hilbert demodulation method is used to analyze the envelope spectrum of the signal processed by MCKD to realize the identification of different types of rolling bearing faults. The analysis results of simulation and measured signals show that the proposed method can clearly extract the single fault characteristic frequency from the composite fault signal, which provides an effective solution for the complex fault characteristic extraction of rolling bearing.