We investigated the quench velocity of superconducting fault current limiter (SFCL) dependent on the source voltage. $YBa_2Cu_3O_7$ (YBCO) thin film was used as the current limiting element for SFCL. The analysis on the quench velocity of SFCL is essential to determine the capacity of circuit breaker (CB) or coordinate with CB. Generally, the quench velocity of SFCL is related with the short-circuit current. To change the short-circuit current, in this paper, the amplitude of the power source voltage is adjusted. Through the fault current limiting experiments, the quench velocity of SFCL was confirmed to increase fast as the source voltage increased. On the other hand, the peak limited current was shown to increase with steady rate of increase.