With the research and development of high temperature superconducting technology, superconducting insulating materials under liquid helium and nitrogen temperature have been gradually taken seriously. Considering the unique operating environment, epoxy resin and PI face the challenge of low temperature. Electrical tree is one of the aging failure phenomena occurring in solid dielectrics. These imperfections could cause the field concentration with the application of high voltage, which results in partial discharges (PD). PD testing is an important quality check for the insulation of HTS cable. This chapter presents a study aimed at clarifying the influence of low temperature, pulse frequency and pulse duration on the electrical tree characteristics in epoxy resin, as well as PD characterization of PI film in LN2. The results show that the number of discharges and the discharge quantity in PI films increase with the increasing of the applied voltage and the defect size. The PD inception voltage decreases when the void defect diameter in PI enlarged and it is higher in LN2 than that at room temperature.