In this paper, the operational characteristics due to the introduction of the superconducting fault current limiter(SFCL) with a peak current limiting function were analyzed in the power distribution system. The parallel structure of the superconducting element can operate the peak current limiting function depending on the transient amplitude of fault current. We studied the operating characteristics of the introduction of the SFCL with a peak current limiting function in the power distribution system. Furthermore, we were analyzed between the SFCL with a peak current limiting function and the protection devices in the power distribution system, through the short circuit experiments.