For the insulation design of a high temperature superconducting(HTS) cable, three kinds of design method were proposed, which used AC and impulse withstand voltage and partial discharge inception strength. However, the designed insulation thickness by AC and impulse could not be applied to cable fabrication process due to much low electrical breakdown strength. The effect of the multi-layered insulation paper was not considered on the previous insulation design and the insulation thickness by partial discharge inception strength could be applied only. In this paper, the electrical breakdown characteristic, which considered the effect of multi-layered of LPP, was investigated to design the insulation thickness.