A research on several characteristics such as volume breakdown and surface discharge of insulators for a termination of power transmission class HTS cable was performed. We investigated the surface discharge of glass fiber reinforced plastic (GFRP) under air, cryogenic nitrogen gas and nitrogen gas media. The breakdown characteristics of these media were studied. Experimental results revealed that flashover voltage greatly depends on pressure, temperature, the kinds of insulating media and voltages, but it is slightly affected by shape and material of electrode. The breakdown voltage of liquid nitrogen, cryogenic nitrogen gas and nitrogen gas deeply depends on the shape and dimension of electrode, kinds of voltages and pressure. Moreover, the breakdown voltage of cryogenic nitrogen gas and flashover voltage of GFRP in the cryogenic nitrogen gas is also influenced by temperature and vapour-mist density of the gas.