The dynamic response of a Duffing system from self-induced resonance to system resonance is studied in this paper. From numerical simulation, it is found that the system response gradually transits from self-induced resonance to system resonance with the increase of the pulse amplitude of the signal. In order to describe this process, we define the quality factor of the system response. With the evolution from self-induced resonance to system resonance, the quality factor gradually increases from 0 to 1. Then, based on the evolution, a novel method is developed to evaluate the severity of rolling bearing early damage. The results show that the method can be used not only to describe the process of a rolling bearing from healthy to damaged, but also to evaluate the severity of the early damage of a rolling bearing. The quality factor is a key index to reflect the severity of a rolling bearing. In addition, the sensitivity of the quality factor is superior to other traditional indices formerly used in the early damage evaluation. The effective method gives a new way for rolling bearing early damage evaluation.