The transformer is expected to be an essential component of a superconducting fault current limiter (SFCL) for both the increase of its voltage ratings and the simultaneous quench due to different critical current between high-$T_C$ superconducting (HTSC) elements comprising the SFCL. However, in order to perform the effective current limiting operation of the SFCL, the design for the SFCL considering the hysteresis characteristics of the iron core is required. In this paper, the influence of the hysteresis characteristics of the iron core comprising the transformer type SFCL on its current limiting characteristics was investigated. Through the comparative analysis on the hysteresis curves due to the ratio of the turn number between the 1st and the 2nd windings of the transformer, the proper design condition for the ratio of the turn number to achieve the effective current limiting operation of the transformer type SFCL could be obtained.