In this study, we discussed the characteristics of breakdown and surface flashover of FRP in L$N_2$ for applying it to spacer of a superconducting power equipment. Fiberglass reinforced plastic(FRP) has high breakdown puncture strength and has high mechanical strength. So the research of its dielectric properties have been conducted in liquid nitrogen($LN_2$). We measured breakdown voltage of FRP and distinguished four types of surface flashover along solid insulator with arrangement of electrodes and measured the surface flashover voltages of each types of electrode arrangement. The type of a electrode set at the back of the insulator showed the worst dielectric property. The property of surface flashover depending on pressure was tested.