A novel methodology for the fault diagnosis of rolling bearing in strong background noise, based on sensitive intrinsic mode functions (IMFs) selection of ensemble empirical mode decomposition (EEMD) and adaptive stochastic resonance, is proposed. The original vibration signal is decomposed into a group of IMFs and a residual trend item by EEMD. Constructing weighted kurtosis index difference spectrum (WKIDS) to adaptively select sensitive IMFs, this method can overcome the shortcomings of the existing methods such as subjective choice or need to determine a threshold using the correlation coefficient. To further reduce noise and enhance weak characteristics, the adaptive stochastic resonance is employed to amplify each sensitive IMF. Then, the ensemble average is used to eliminate the stochastic noise. The simulation and rolling element bearing experiment with an inner fault are performed to validate the proposed method. The results show that the proposed method not only overcomes the difficulty of choosing sensitive IMFs, but also, combined with adaptive stochastic resonance, can better enhance the weak fault characteristics. Moreover, the proposed method is better than EEMD and adaptive stochastic resonance of each sensitive IMF, demonstrating the feasibility of the proposed method in highly noisy environments.