The aim of this study is to investigate the dynamic responses of a rub-impacting rotor system. A response integration method is applied to analyze bifurcation and chaotic responses for the rub-impacting rotor system. This integration method numerically integrates the distance between state trajectory and the origin in the phase plane during a specific period. It provides a quantitative characterization of system responses and can replace the role of the traditional stroboscopic technique (Poincaré section method) to observe bifurcations and chaos of the rotor system with rub-impact. According to the result comparisons from the rub-impacting rotor system, it is inferred that during Poincaré section method being applied to be analyzed the system response periods, the sampling points on Poincaré section might be too close to cause disturbances to analyze if the system response is a high-order sub-harmonic vibration. Thus, the misjudgments for system response periods will be made. The simulation results, however, show that the high-order subharmonic and chaotic responses and their bifurcations can be observed effectively.