The low frequency response of oil paper insulation is very important for the diagnosis of damp and aging of insulation. In view of the lack of analysis methods for low-frequency response data and the imperfection of the corresponding equivalent circuit model, the Kramers-Kronig transform is used to separate the conductance, infinite frequency capacitance and relaxation process in the frequencydomain dielectric spectrum of oil paper insulation. The Dissado-Hill model based on multi-body theory is introduced to fit the lowfrequency relaxation process. A new oil paper insulation model is formulated, which is the equivalent circuit model of paper insulation for low frequency response. Finally, the low frequency response data of oil paper insulation samples with different moisture content are modeled and analyzed. Experimental results show that the Kramers-Kronig transform can effectively decouple the relaxation process, conductivity process and infinite frequency capacitance of oil paper insulation. The goodness of fit of reconstructed spectral lines of the low-frequency response model for samples with different moisture content is more than 0. 98, which evaluateds the accuracy of the model. There is an exponential function relationship between the amplitude of low-frequency diffuse polarizability χ LFD ( 0) and micro water content. The goodness of fit is as high as 0. 99, which can be utilized as a new characteristic quantity for quantitative evaluation of moisture content of oil paper insulation. It provides a new idea for diagnosis of moisture affected state of oil paper insulation.