The superconducting fault current limiter (SFCL) with a peak current limiting function according to the initial fault current with the different amplitudes was suggested. The proposed SFCL, which consists of two limiting components, causes only the first superconducting element among two limiting components to be quenched in case that the initial fault current with the lower peak amplitude happens. On the other hand, the initial fault current with the higher peak amplitude makes both the superconducting elements of two limiting components to be quenched, which contributes to the peak current limiting function of the SFCL. To confirm the fault current limiting operation of the proposed SFCL, the short-circuit tests of the SFCL according to the fault angle were carried out and its effective fault current limiting operations could be discussed.