In this paper, we analyzed the fault current performance in a $high-T_{c}$ superconductor(HTS) which was installed on flux-lock reactor with an external magnetic field coil covering the HTS. In this HTS fault current limiter using flux-lock concepts, the initial limiting current level can be controlled by adjusting the inductance of the coils. Furthermore, the current limiting characteristics of $high-T_{c}$ superconducting FCL can be improved by applying the external magnetic field into the $high-T_{c}$ superconductor. This paper discusses current limiting performance according to the inductance of the coil 1 in two cases with ac magnetic field coil or not and suggests the methods to improve the current limiting factor $P_{limit}$, which is defined as the ratio of the limited current $I_{FCL}$ at the current limiting phase to the prospective short -circuit current $I_{PSC}$.TEX> PSC/.