Spectral kurtosis is an effective tool for extracting the impulse response from vibration signals with strong background noise. This paper presents an adaptive spectral kurtosis filtering method to overcome the problem of window width adaptive selection. The center frequency of the filtering wavelet window is obtained using wavelet correlation filtering, and the adaptive selection of optimal Morlet wavelet window width can be obtained based on the principle of the maximum spectral kurtosis. The effectiveness of the proposed method is verified through the transient extraction form strong background noise and further proved by comparison with adaptive spectral kurtosis based on merging windows. For the bearing fault vibration signal detection, the proposed method is applied in the extraction of the transients caused by the fault, thus proving the method′s effectiveness in extracting the feature signal for bearing fault detection.