Partial discharge at the oil-paper interface is one of the main reasons for the failure of oil-paper insulation in oil-immersed transformers. In this article,based on the numerical model of multi-branching streamer discharge,a multi-branching streamer discharge model in oil-paper insulation system is constructed by further considering the charge transport characteristics of oil-paper interface. The surface discharge characteristics under the influence of the dielectric constant ratio between natural ester insulating oil and insulating paper,and the spacing between needle electrode and paperboard are studied by finite element method,respectively. The results show that the distance between the needle electrode and the paperboard,and the dielectric constant ratio of insulating oil and insulating paper both significantly affect the streamer branching. The smaller the clearance between the needle electrode and paper-board is, the more serious the inhibition of streamer branches at the oil-paper interface is,which resulting in the streamers near the oil-paper interface are more significant effect on the propagation of the z-axis streamer. When the dielectric constant of the insulating oil is larger than that of the paperboard,the development and branching of the streamer in the oil will be more significant. On the contrary,the streamer is more likely to develop along the surface of the paperboard and accumulate charge at the oil-paper interface.