In this study, the frequency-domain dielectric spectrum (FDS) of oil-paper insulation at various aging states was analyzed from the perspective of system stability. The results of the study revealed that: 1) as the aging increased, the closed-loop poles of both the insulation oil and the insulation paper move regularly in the same direction; what is more, the step response speed of the system was increasing, which corresponded with the step response rise time and regulation time of system gradual shorten; 2) the presence of rise time is a characteristic of insulation paper, which is completely different from that of insulation oil in time-domain step response; and 3) for the step response rise time of insulation paper, step response regulation time and closed-loop mean poles of insulation paper, and step response regulation time and closed-loop mean poles of insulation oil, the above parameters were revealed to be the characteristic parameters of aging state evaluation.