This paper presents a novel signal processing scheme, bandwidth empirical mode decomposition, and adaptive multiscale morphological analysis (BEMD-AMMA) for early fault diagnosis of rolling bearings. In this scheme, we propose a bandwidth based method to select the best envelope interpolation method. First, multiple envelope algorithms are defined and separately subtracted from the original data to obtain the preintrinsic mode functions (PIMFs). Second, an IMF with the smallest frequency bandwidth is selected to be the optimal IMF (OIMF). Third, this OIMF is subtracted from the original signal, and then repeat the sifting process until the residual is a constant or monotonic. Since the OIMF has the smallest frequency bandwidth, the mode mixing phenomenon can be significantly weakened. After that the OIMFs with clear fault information are used to construct the main component of the original signal. Then, the AMMA is introduced to demodulate the constructed main component. Simulation and experimental vibration signals are employed to evaluate the effectiveness of the proposed method. Results show that the proposed method outperforms EMD-AMMA, ensemble empirical mode decomposition-AMMA, and generalized empirical mode decomposition-empirical envelope demodulation in detecting early inner race fault.