Compound fault diagnosis of rolling bearings under complex interference is always considered to be a great challenge in condition monitoring of rotating machinery. In order to provide an adaptive solution for this problem, a novel signal decomposition method named fast amplitude modulation mode decomposition (FAMMD) is presented in this paper. The main advantages of the proposed method are that it does not require any prior knowledge, is robust to strong background noise and has high computational efficiency. FAMMD applies spectral trend to decompose a signal into a series of initial modes, after which characteristic harmonic intensity is calculated via harmonic intensity spectrum to quantify the most dominant cyclostationary element in each mode. Based on different ratio, the fault number in the signal is determined while characteristic frequencies in fault modes are also estimated, so as to further guide the local spectral amplitude modulation for nonlinear separation of fault characteristics. Simulated analysis and experimental studies demonstrate the potential of FAMMD in realizing adaptive and efficient extraction of bearing compound fault characteristics under strong noise. Comparisons with other state-of-the-art methods further highlight its superiorities.