In the traditional Lempel-Ziv complexity（LZC）calculation process，the binary processing changes the dynamic characteristics of the original sequence and lead to the low computational efficiency. Combined with the impact characteristics of bearing faults，a compound dictionary matching pursuit（CDMP）algorithm is proposed，and variable scale Lempel-Ziv complexity（VL?ZC）analysis is combined to evaluate the damage degree of inner and outer rings of rolling bearings. CDMP is used to reconstruct the original signal and detect the periodic impact component in the signal. According to the impact amplitude，the reconstructed signal is divided into bearing fault impact area and impact attenuation area. After the impact in the signal is binarized by variable scale，it is regarded as the basic element of iteration and the VLZC index is calculated by ergodic search method. According to the 3σ principle，the VLZC indexes of the inner and outer rings are given. The VLZC value range of damage degree and BP neural network are introduced to classify the damage degree intelligently. The results show that the new method can effectively reduce the noise，retain the periodic impact characteristics in the signal，suppress the non-impact components，improve the iterative calculation efficiency，and effectively evaluate the damage degree of the inner and outer rings of rolling bearing.