A 154kV class high-temperature superconducting (HTS) power cable system is developing in Korea. For insulation design of this cable, it is important that study on cryogenic electrical insulation design to develop the cold dielectric type HTS cable because the cable is operated under the high voltage environment in cryogenic temperature. Therefore, this paper describes a design method for the electrical insulation layer of the cold dielectric type HTS cable adopting the partial discharge-free design under ac stress, based on the experimental results such a ac breakdown strength, partial discharge inception stress, $V_{ac}$-t characteristics, $V_{imp}$-n characteristics, and impulse breakdown strength of liquid nitrogen/laminated polypropylene paper (LPP) composite insulation system in which the mini-model cable is immersed into pressurized liquid nitrogen.