Polypropylene laminated paper (PPLP) and Kraft paper have been studied as multi-layer insulation for high temperature superconducting cable. The experiment was conducted with AC and impulse voltages. Short-term and long-term breakdown of insulation samples were investigated. The experimental results show that the breakdown voltage becomes smaller in the order of PPLP, PPLP/Kraft and Kraft, but the lifetime index increases with the presence of Kraft layer in the multilayer insulation. In addition, the position of PPLP layers has a significant effect on the breakdown voltage of PPLP/Kraft samples under positive impulse voltage. Finally, breakdown mechanism of PPLP/Kraft composite insulation was suggested. Partial discharges in butt-gaps and in the porous structure of insulation layers combined with electric discharges on the surface of these layers are considered to be main factors causing the puncture of multi-layer insulation.