The existing cantilever FBG acceleration sensor can be subjected to uneven force due to the optical fiber surface adhesion, and can not work in the complex environment of temperature change and vibration. In order to solve such problems, a dual fiber-cantilever structure FBG acceleration sensor is proposed. The influence of structural parameters on the sensitivity and natural frequency of the sensor was analyzed theoretically, and the static stress and modal simulation analysis was carried out by ANSYS finite element analysis software. Finally, a test system was built to test the performance of the sensor. The results show that the natural frequency of the acceleration sensor is 84.86Hz, and it has a flat sensitivity response in the low frequency range of 15~60Hz. The dual optical fiber can effectively eliminate the influence of temperature changes while increasing the sensitivity of the sensor, obtaining the acceleration sensitivity of 156.70pm/g and the linearity of 99.38%. The rigid beam effectively increases the stability of the structure, and the lateral crosstalk within the working frequency band is -26.97dB.