Centrifugal compressors are key parts of medium and small aircraft engines, the flow instabilities of centrifugal compressors have become the bottleneck of the developments of engines. It is vital to investigate the dynamic mode characteristics of flow instabilities in centrifugal compressors for solving the issues. In this study, unsteady full annular simulations of the centrifugal compressor flow are firstly implemented. It is found that the flow instability of the compressor primarily arises in the impeller. To capture the dominant transient modes in process of flow instabilities and accurately describe their temporal evolutions, a modified dynamic mode decomposition method (DMD-TC) is adopted to analyze the dynamic mode characteristics, which was proposed in our previous study. The results show that perturbations in the impeller can be mainly classified into three categories: impeller-diffuser interactions, self-excited perturbations, and vortex-induced perturbations. In detail, the modes induced by the impeller-diffuser interactions and self-excited perturbations are intrinsic modes, and they reflect the inherent flow unsteadiness in the impeller. On the one hand, the vortex-induced perturbations couple with the self-excited ones, which affect the spatial structures of modes induced by self-excited perturbations. The coupling effects enhance with the reduced mass flow rate, and the “resonance” effect might be excited. As a result, the mode of 4 RF (rotor frequency) grows during rotating stall process (RSP), which is a typical characteristic of rotating stall in the impeller. On the other hand, the vortex-induced perturbations emerge as different characteristic modes, due to the variant vortex structures with the mass flow rate. During the RSP, the growth of low-frequency characteristic modes is another typical feature of rotating stall in the impeller.