The present paper proposes a new type fault current limiter (FCL), which consists of a high T-c superconducting (HTS) element, three coils wound on the same core, and a magnetic field coil covering the HTS element. In this FCL, the initial limiting current level can be controlled by adjusting the inductances of the coils. Furthermore, an external a.c. magnetic field is applied to the HTS element to get higher resistance in the current-limiting phase. A current-limiting experiment by a model FCL was carried out, and the limiting performance of the FCL was observed. Both the initial limiting current level and the limiting impedance could be increased in this FCL compared with the corresponding values of the HTS element itself.