In this study, the frequency domain dielectric spectrum 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’s 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) the step response rise time of insulation paper, step response regulation time and closed-loop mean poles of insulation paper, 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.