A passive and non-contact current sensor based on giant magnetostrictive material (GMM) and fiber Bragg grating (FBG) is proposed. The position of reference GMM, the size and direction of the reserved expansion space of the magnetic concentrator, the side length of the cross section and the length of the upper opening are analyzed and optimized by COMSOL software, so as to ensure the dense and uniform distribution of magnetic force lines in the bonding area of the sensing FBG. Finally, the temperature independence of the current signal is measured by the double grating-intensity demodulation system. The alternating current (AC) and direct current (DC) characteristic test of the sensor shows that the sensitivity of the sensor is 249.75 mV/A under the DC input of 0.8--3.5 A, and the linear correlation coefficient is as high as 0.9942. Under the action of a bias current of 1.6 A, the sensor has a good response ability to the sinusoidal input signal of 50 Hz--6.5 kHz. At the same time, the test of the temperature characteristic of the sensor shows that the double grating-intensity demodulation method can eliminate the influence of ambient temperature on the output voltage to a great extent. The sensor proposed in this paper has the advantages of small size, simple structure, stable performance, and low cost, and has temperature-independent characteristics.