High temperature superconductor can only be applied against an engineering specofication that has to be determined for each particular application form the design requirements for economic viability and for operation margins in service. However, in order to realize the HTS transformer, it is necessary to establish the high voltage insulation technique in cryogenic temperature. Therefore, the composite insulation of double pancake coil type transformer are described and AC breakdown voltage characteristics of liquid nitrogen(LN$_2$) under HTS pancake coil electrode made by Bi-2223/Ag are studied. The Breakdown of LN$_2$ is dominated electrode shape and distance. The influence of pressure on breakdown voltage is discussed with th different electrode. For the electrical insulation design of turn-to-turn insulation for the HTS transformer, we tested breakdown strength of insulation sheet under varying pressure. And we investigated surface flashover properties of LN$_2$ and complex conition of cryogenic gaseous nitrogen(CGN$_2$) obove a LN$_2$ surface. The surface voltage of GFRP was measured as a function of thickness and electrode distance in LN$_2$ and complex condition of CGN$_2$ above a LN$_2$ surface. this research presented information of electrical insulation design for double pancake coil(DPC) type HTS transformer.