The iron core, which comprises the superconducting fault current limiter (SFCL) using magnetic coupling of coils, can be operated in the saturation region, especially at the initial fault period. This operation of the iron core in the saturation region deteriorates the fault current limiting operation of the SFCL. To solve the saturation problem of the SFCL using magnetic coupling of coils, the iron core with two magnetic paths, which has an air-gap in one of them, was adopted. In this paper, the hysteresis characteristics of SFCL using magnetic coupling of coils, which were wound in the iron core with two magnetic paths, were analyzed. Through comparative analysis on the hysteresis characteristics of the iron core comprising SFCL, the hysteresis characteristics of the iron core with two magnetic paths were confirmed to be kept in the non-saturation region during the fault period and thus, the effective fault current limiting operation of the SFCL using the magnetic coupling of coils could be performed.