Due to the mutual coupling between sub-faults in the case of compound faults in rolling bearings, coupled with external noise, energy attenuation during information transmission, etc., the acquired fault information is usually very weak and complex. This greatly increases the difficulty of extracting features from bearing compound faults. To further enhance the accuracy of fault feature extraction and achieve precise identification of rolling bearing compound faults, this paper presents an innovative compound fault diagnosis method that integrates variable step-size multiscale weighted Lempel-Ziv complexity (VMW-LZC) and intrinsic time-scale decomposition (ITD). First, considering that the traditional Lempel-Ziv complexity (LZC) method can only extract single-dimensional fault information without thoroughly exploiting fault characteristics, we optimize the coarse-graining process of proper rotation components (PRCs) after ITD using a variable step-size multiscale strategy. Additionally, LZCs obtained from variable step-sizes in each scale are fused and reconstructed using a weighted method. Meanwhile, multiple variable step-size multiscale LZCs are combined into a new signal evaluation index, VMW-LZC. In addition, with the new signal evaluation index VMW-LZC, the optimal PRC which is best representative of fault characteristic information is chosen. Furthermore, frequency spectrum of autocorrelation function of optimal PRC is used to identify multiple faults of bearings. To exemplify the efficiency of presented method, a comparison has been made among the optimal PRC chosen by the methods with VMW-LZC, traditional LZC (T-LZC), multiscale LZC(M-LZC), and classical kurtosis as signal evaluation indexes. The result has indicated that fused signal evaluation index VMW-LZC can actualize more precise option of sensitive fault component signals and the proposed ITD-VMW-LZC method can do a more precise job in identifying a compound fault of bearings.