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This paper describes a study to determine the optimal parameter of a resistive superconducting fault current limiter (SFCL) applied to an electric power grid. The resistive SFCL, which is designed to provide the quick system protection during a fault, affects the entire system by reducing the fault current and improving the transient stability. In order to determine the optimal parameter of the resistive SFCL systematically, the eigenvalue analysis for an entire system is used. Generally, the eigenvalue analysis is useful to evaluate the relationship between parameter of a controller and stability of an electric power system. Therefore, the optimal parameter of the SFCL is determined based on the analysis of eigenvalues corresponding to low-frequency oscillations. Moreover, this optimal parameter obtained by the proposed method is compared with that determined by applying the equal-area criterion. The effectiveness of the optimal parameter for the SFCL is evaluated by time-domain simulation. The results show that the optimal resistive value determined by the eigenvalue analysis improves the damping performance of low-frequency oscillations effectively.