Fiber optic accelerometers have a wide range of applications in low-frequency vibration measurement, such as in earthquake monitoring, disaster early warning, underground resource exploration, and anti-seismic monitoring projects for critical structures like dams and bridges. In response to the current issues of Fiber Bragg Gratings (FBG) accelerometers being insensitive to low-frequency vibration signals and challenging to apply in engineering, a dual straight-wing FBG accelerometer for low-frequency vibration measurement is proposed. Firstly, a sensor model is established and theoretically analyzed. Secondly, the impact of the sensor's main structural parameters on sensitivity and natural frequency is analyzed, and the sensor is simulated using ANSYS. Finally, a prototype of the sensor is developed, and a low-frequency vibration testing system is set up to test the sensor's performance. Experimental results show that the accelerometer has a natural frequency of 39.1 Hz, operates in the 5–22 Hz frequency band, and has a sensitivity of 171.7 p.m./g, a dynamic range of 69.82 dB, and a transverse interference resistance of less than 9.5%. This research provides a new reference for the development of similar sensors.