Fiber optic current transformer (FOCT) can overcomes the disadvantage of traditional electromagnetic current transformer in transient current response, sensitivity and reliability of protective action can be remarkably improved by optimization of dynamic characteristics. The closedloop control algorithm is a main limitation to the detection bandwidth of the FOCT based on the closedloop signaldetecting scheme. The theory analysis and experiment show that the bandwidth of closedloop FOCT is greatly improved by introducing the PID control algorithm. It is of great significance for the promotion and application of fiber current transformer in smart grid protection.