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High temperature superconductor (HTS) is a promising material as current leads for large current applications, because it has zero resistance. However, a single HTS tape has limitation on the capacity of current rating due to the critical current of the HTS tape. Therefore, stacking or parallel structure of the HTS tapes is inevitable in high temperature superconducting current leads (HTSCLs) for large current application. In this paper, several stacking methods with respect to the shape of the current terminal and the structure of the HTS tape are studied and the characteristics of the stacked samples are investigated by experimental analysis. The critical currents of the HTS modules were measured and the conductive heat leakage of a stabilizer layer was calculated. From this analysis, the characteristics of the current distribution and decrease in the critical current of HTS modules with respect to the shape of the current terminal were obtained. Based on the results, the required stacking number of the HTS tapes for certain operating current HTSCLs can be calculated.