The flashover process of the peaking capacitor in the electromagnetic pulse (EMP) simulator is studied based on theoretical analyses and experimental verification in this paper. There are deeper and denser ablation spots on the film surface near the inner core of the destroyed peaking capacitor, while the damage of the outer film is relatively slight, which indicates that the flashover current along the inner film is larger. Besides, the circuit simulation analyses show that the earlier the flashover occurs on the film of the peaking capacitor, the smaller the flashover current. The electric field on the non-conical surface of the capacitor is mainly occupied with normal component. Differently, for the conical surface, the electric field on the outer layer is dominated by the normal component and the parallel component is the main part on the inner layer. It is considered that the flashover on the conical surface originates from outer layers and develops gradually to the inner until the flashover penetrates through all layers. Furthermore, the images of flashover show that the flashover firstly occurs on the outermost layers and develops to the inner layers with the increase of the voltage. For such special structure of the peaking capacitor, the parallel component of electric field is more likely to facilitate the flashover under nanosecond pulse. These results may exhibit specific reference implication in the design of insulation for the peaking capacitor used in EMP simulator.