According to our previous experiment, oil flow electrification is closely related to the space charge behaviors in oil-paper insulation system under DC voltage. In this paper, we present a new numerical method to estimate the streaming current in a rectangular paper duct under DC voltage. For the simulation model, we consider the case of laminar flow in a sample of two layers of oil-impregnated-paper and oil between two electrodes. Moreover, on the basis of bipolar transport model, the effects of charge injection and ion mobility are taken into account. Numerical results show that the amplitude of streaming current is always enhanced with the increase of applied voltage. Compared to the result estimated by AC simulation model, the result of our simulation model has larger amplitude, and the consequence of our numerical simulation is in accordance with the experimental results.