The breaking capacity of circuit breakers could be no more increased in the electric power system. This is because the fault current increases due to continuous increases in electric power demand and facilities. To solve the problem, it is necessary to come up with an alternative. The superconducting fault current limiter (SFCL) has received an attention among various alternatives. The SFCL effectively reduce a fault current in cooperation with a power circuit breaker. A various types of the SFCL are suggested and a study on them have been progressed. As a result of it, the SFCL can be applyed to the electric power system in the near future. But, a study on recovery behaviors of the SFCL is not enough for applying to the electric power system. If the superconducting elements do not completely recover to the superconducting state after fault operation, it might be a breakdown of the superconducting elements due to heavy power burden and it gives an bad influence on the working of other electric devices. Additionally, the distribution power system has reclosing operation such as open-0.3sec-closed/open-3min-closed/open procedure. So we need to study more about improvement of the recovery behaviors of the SFCL. In this paper, we analyzed the recovery behaviors of a flux-coupling type SFCL according to reclosing operation when a single line-to-ground fault occurred and we compared recovery behaviors of the SFCL with and without a neutral line between secondary reactors and superconducting elements. Also, the flux-coupling type SFCL has advantageous for increases of capacity by controlling the variation in turn ratios between two reactors. Consequently, when the number of turns of the secondary reactors increased, the power burden of the superconducting elements was bigger due to the increase of impedances of the secondary reactors. To distribute the power burden, two superconducting elements connected in series and the balanced quenching of the superconducting elements was induced by connecting a neutral line.