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In superconducting magnetic energy storage system (SMES), the current lead is the conductor that connects the room-temperature power supply and the low-temperature cryogenic superconducting magnet. It is the main source of thermal leakage in the system. In order to decrease the thermal leakage, it is necessary to analyze the thermal loss of the current lead and optimize the lead dimension. Because of the complex heat transfer condition, many simplified assumption will be taken when using analytic method, which will bring inaccuracy. The variation of heat condition and material properties will be generally considered in finite element method, which is more suitable for calculating lead heat leakage. The heat leakage analysis and optimization design of 35kV/2kA current lead in SMES are presented in this paper. Based on initial range of current lead acquired from traditional method, the 2D model of current lead could be built and the electric-thermal coupling analysis will be executed with finite element method. Considering the lead heat leakage result of electric-thermal coupling analysis as the target variable, the ratio of current lead length and cross sectional area (L/A) at the minimum heat leakage will be got when the structure condition of current lead optimized.