Superconducting power lead equipment for epoxy insulation, such as high-temperature superconducting DC power or liquefied natural gas energy pipelines, as well as high-temperature superconducting cables, has long been used in extreme environments, from liquid nitrogen temperatures to normal temperatures. It is easy to induce surface discharge and flashover under the action of strong electric field, which accelerates the insulation failure of current leads. In this paper, two-dimensional nano-material GO was used to control the electrical properties of epoxy resins. The DC surface discharge and flashover characteristics of the prepared epoxy resin–GO composite insulation materials were tested at room temperature with liquid nitrogen. The surface discharge mechanism of the epoxy resin–GO composite insulation materials was analyzed. The experimental results show that the insulation properties of epoxy composites doped with GO changed. Among them, the surface flashover voltage of 0.05 wt% material is the best, which can inhibit the discharge phenomenon and improve its insulation properties in extreme environments, from room temperature to liquid nitrogen temperature. It is found that the development process of surface discharge of composite insulating materials under liquid nitrogen is quite different from that under room temperature. Before critical flashover, the repetition rate and amplitude of surface discharge remain at a low level until critical flashover. Furthermore, the voltage of the first flashover is significantly higher than that of the subsequent flashover under the action of the desorption gas on the surface of the composite insulating material and the gasification layer produced by the discharge. Given that the surface flashover voltage of 0.05 wt% epoxy composite is the best, the research and analysis of 0.05 wt% composite is emphasized. In the future design of superconducting power lead insulation, the modification method of adding GO to epoxy resin can be considered in order to improve its insulation performance.