The research history and current status of high temperature superconducting (HTS) cable in the world are summarized, and the basic structure and insulation requirements of HTS cable body are introduced. Then, the structure and problem of the main insulation for HTS cable are analyzed. For liquid nitrogen ( LN₂ ) and several solid insulation materials under low temperature applied in HTS cables, related researches are put forward separately on their dielectric property under low temperature. It can be concluded that, in LN₂, the breakdown strength of insulation material is higher in DC field than that in ac field; the breakdown strength of polyimide is higher than that of polypropylene laminated paper (PPLP) in both ac and dc field; low temperature can suppress the growth of the electrical tree in epoxy resin.