Due to the coupling of multiple fault feature information and contamination of heavy background noise, it is a challenging task to accurately identify Rolling Bearing Compound Fault (RBCF). A method for isolating and identifying the RBCF is proposed by integrating the Adaptive Periodized Singular Spectrum Analysis (APSSA) with Rényi entropy (RE). The adaptive selection of embedding dimension of Hankel matrix in APSSA without setting parameters empirically is proposed, and a selection criterion for singular values is established to preprocess the vibration signals of rolling bearing and enhance fault periodic component. A RE-based threshold value is introduced to further isolate and decouple the impulse segments of vibration signal in the time domain. Considering inner raceway fault, outer raceway fault, ball fault and skidding, a comprehensive simulation model of compound fault is constructed by the response mechanism of different excited resources. Simulated and experimental data are applied to validate the effectiveness and practicability of proposed method. The results demonstrate that RBCF can be identified correctly by the proposed method under strong background noise.