Modeling of dielectric relaxation function φ(t) by a distribution of exponential decay functions is advantageous due to its monotonically decreasing property which ensures that φ(t) is integrable over any period of time. Several equivalent circuits based on simple combination of energy storing and dissipating elements are available in literature which are capable of modeling φ(t). One of the widely used two-parameter equivalent circuit for dielectric response modeling of various polymeric dielectric as well as oil-paper insulation is the Maxwell ladder structure. In this paper it is shown that for more accurate modeling and better understanding of the dielectric response of complex insulation system like oil-paper insulation of high voltage equipments operating under temperature gradient, modification of Maxwell model is necessary. The proposed model, similar to the classic Maxwell circuit, is also composed of a number of parallel branches, but unlike the former, the proposed model considers each of the parallel branches to be composed of not just one but a number of exponential functions.