Optical fiber current sensors are widely used in the online monitoring of a new generation power system because of their high electrical insulation, wide dynamic range, and strong anti-electromagnetic interference ability. Current sensors, based on fiber Bragg grating (FBG) and giant magnetostrictive material, have the advantages of high reliability of FBG and high magnetostrictive coefficient of giant magnetostrictive material, which can meet the monitoring requirements of digital power systems. However, giant magnetostrictive materials are expensive, fragile, and difficult to mold, so giant magnetostrictive composite materials have replaced giant magnetostrictive materials as the sensitive elements of sensors. High sensitivity, high precision, wide working range, low response time, and low-cost optical fiber current sensors based on magnetostrictive composites have become a research hotspot. In this paper, the working principle of the sensor, the structure of the sensor, and the improvement of magnetostrictive composite materials are mainly discussed. At the same time, this paper points out improvements for the sensor.