The chatter incubation stage exists between stable cutting and chatter burst. Chatter behaviors contained in the signals during this stage are deemed as the typical weak features. The traditional method that combines ensemble empirical mode decomposition （EEMD） with singular value decomposition （SVD） is employed to denoise the signal of chatter incubation stage， despite which issues like insufficient denoising and weak feature loss can also be found. Therefore in this paper， the denoising mechanism of EEMD is improved by introducing power spectral density （PSD） and constant coherent function （CCF）， rendering intrinsic mode functions （IMF） components of the weak features effectively extracted. Next， with the help of pooling principle （PP）， the complexities of the extracted IMF components are reduced， following combined SVD to realize the blocking-based denoising process. Consequently， the noises contained in the weak features can be suppressed efficiently. Finally， by coupling the improvements mentioned above and reconstructing signals， the general frame of a denoising method based on improved EEMD-SVD （IES） can be established. The IES and the traditional EEMD-SVD are respectively adopted to denoise Rossler chaotic signals. According to the assessment indexes including signal-to-noise ratio， mean-square error， and smoothness， the proposed IES method is quantitatively verified in terms of denoising efficiency and weak feature fidelity. The proposed IES method is then applied to denoise the milling force signals of the chatter incubation stage involved in an axial depth varying milling experimentation. The results show that the proposed method can not only suppress the noise of the chatter incubation stage significantly， but also guarantee the fidelity of the weak chatter feature.