The magnetic field application effect on resistance of a high-$T_c$ superconducting (HTSC) element comprising a flux-lock type superconducting fault current limiter (SFCL) was investigated. The YBCO thin film, which was etched into a meander line using a lithography, was used as a current limiting element of the flux-lock type SFCL. To increase the magnetic field applied into HTSC element, the capacitor was connected in series with a solenoid-type magnetic field coil installed in the third winding of the flux-lock type SFCL. There was no magnetic field application effect on the resistance of HTSC element despite the application of larger magnetic field into the HTSC element when a fault happened. The resistance of HTSC element, on the contrary, started to decrease at the point of four periods from a fault instant although the amplitude of the applied magnetic field increased.