The failure of cooling system in Superconducting Fault Current Limiter(SFCL) increases the impedance of superconducting device, and due to malfunction of inner switches the SFCL opens the distribution system inadvertently when required to do so. In this paper, the ground fault and short circuit fault were classified as active failure and the open circuit fault was passive failure. A reliability model of SFCL considers the passive failure as well as active failure, and in the case study the reliability indices of distribution system are evaluated. It is possible that the reliability evaluation excluded passive failure makes the customers reliability seem so worse than it really was. Therefore, the reliability models of SFCL must include the active failure and passive failure together to evaluate the reliability of distribution system connected SFCL.