A sensitive feature extraction method is proposed to describe the weak state of rolling bearing. It combines the singular value decomposition (SVD) with the ensemble empirical mode decomposition (EEMD). The Hankel matrix is reconstructed by phase space reconstruction of the collected signal to improve the quality of signal failure. The order of noise reduction is determined according to the singular value difference spectrum of the matrix. The noise-reduced signals are decomposed into 11 intrinsic mode functions (IMF) and one residual using EEMD. According to the established kurtosis-mean square error criterion, one of the most effective states sensitive IMF is selected, and its corresponding Teager energy operator (TEO) is calculated, The identification of weak failure mode of rolling bearing is realized by Fourier transform of TEO. The new method is compared with the traditional EEMD-Hilbert method and EEMD-TEO method in case of the opening rolling bearing fault signal of the US west reserve university. The results show that the sensitive features extracted by this method can accurately identify the cycle frequency of rolling bearing fault and accurately identify the fault type, which provides an effective method for the weak feature extraction of rolling bearing.