The development of high temperature superconducting (HTS) dc cable system has been promoted for the land long-term high-capacity power transmissions, submarine cables and renewable energies. Polypropylene laminated paper (PPLP) has been widely used as insulating material for HTS cable. To develop the PPLP-insulated dc cable, it is important to study the dc, dc polarity reversal and lightning impulse characteristics at a cryogenic temperature. In this paper, we discuss the electrical insulation characteristics of PPLP-insulated mini-model cable. We investigate the dc, impulse breakdown strength, dc polarity reversal, and dc voltage (V)-numbers of dc polarity reversal (N). Also, based on these results, the insulation design of 250 kV class HTS dc cable is performed.