A fiber Fabry-Perot interferometric sensor for the measurement of current flowing into a small fuse have been studied. The proposed current sensor was fabricated with a fiber Fabry-Perot interferometer attached close to a fuse line inside a small fuse. The fiber Fabry-Perot interferometer used in the experiment had the 10 mm cavity length and the 3.5 % reflectance mirrors. The phase shift of the output signal of the current sensor was proportional to the square of current applied to the fuse and the sensitivity of the current sensor was 0.87 degree/$mA^{2}$. The experiment results show that this sensor can be used for measuring current flowing into the fuse.