We investigated the quench characteristics of a flux-lock type superconducting fault current limiter (SFCL) depending on the methods of the serial and parallel connections between the superconducting elements. The flux-lock type SFCL consists of two coils. The primary coil is wound in parallel to the secondary coil through an iron core, and the secondary coil is connected to the superconducting elements in series and parallel. In this paper, the analyses of voltage, current, and resistance of the superconducting elements connected in serial and parallel were performed to increase the power capacity of the flux-lock type SFCL. A part of the superconducting elements was not quenched in $2{ imes}2$ serial connection between the elements and then the power burden of the quenched elements was increased. However the elements with $2{ imes}2$ parallel connection was all quenched. This means that the power burden of each superconducting element can be reduced under the same conditions. We found that $2{ imes}2$ parallel connection was more profitable for the current limiting effects and the increase of the power capacity.