Superconducting magnetic energy storage (SMES) has attracted a great deal of interest from the viewpoint of energy saving. The magnet of conduction-cooled high temperature superconducting (HTS) SMES is cooled down by a cryocooler. One of the most important problems to be assured the protection of magnet and cryocooler is breakdown at cryogenic temperature. In this study, we investigated insulation materials such as Kapton, Aluminum Nitride(AIN), Alumina($Al_2O_3$), glass fiber reinforced plastics(GFRP) and vacuum in cryogenic temperature. Also, we analyzed statistically the Weibull distribution of breakdown voltage.