Advanced current measurement technology is one of the key technologies to realize smart grid. The current sensor based on the giant magnetoresistance (GMR) effect has the advantages of small size, high sensitivity, high precision, low cost, and high integration, but the range is limited. In order to expand the range of the current sensor, this paper proposed a novel transient GMR current sensor with a damping coil on the magnetic ring. The theoretical model was deduced and analyzed to calculate the current range of the sensor. The frequency response characteristics and transient current response of the proposed sensor were measured, and the influence of the number of turns and resistance of the damping coil on the performance of the sensor was summarized. Compared with the current sensor without damping coil, the transient current range of the new current sensor with 315 turns of damping coil was expanded by 5.23 times, while the DC range and sensitivity were kept unchanged. The new current sensor can thus adapt to the DC and transient current measurement requirements of smart grids.