Development of the power industry, especially in the field of high-power electricity, is limited by the insulating materials. The main problem of power generation equipment, especially ultra-high-voltage and high-power equipment, is the ability of insulating materials to withstanding voltage. Epoxy resin (EP) is widely used in the power industry. Therefore, it is necessary to improve the performance of EP and demonstrate an energy model of material electrical breakdown. EP has excellent insulation properties, yet poor toughness. By doping with nanomaterials, the toughness of the matrix can be improved on the premise of having little influence on insulation performance. In this paper, two kinds of nanomaterials were added into the matrix, namely multi-walled carbon nanotubes (MWCNTs) and organically modified montmorillonite (OMMT). MWCNTs are conductive, and the insulation properties of EP will be adversely affected if doped in large quantities. OMMT is a nanomaterial with lamellar structure. The toughness of EP can be improved by being doped with OMMT without adverse effect on the insulation performance. Various factors affecting the electric field strength and dielectric properties are analyzed, and models of electric and thermal breakdown are established. In addition, by observing the phenomena of material after breakdown, the energy relation equation of breakdown is re-established.