Vibration detection holds significant research importance and practical value in fields such as aerospace and geology. Fiber Bragg grating (FBG) based vibration sensors have emerged as a major research focus in the field of vibration measurement due to their compact size, resistance to electromagnetic interference, and capability for quasi-distributed measurement. A novel FBG based vibration sensor with a symmetrical structure is proposed in this paper, which is applicable for low-frequency vibration detection. The mathematical model of the sensor is established, and its key parameters such as resonant frequency and sensitivity are analyzed theoretically. Furthermore, structural simulation research and vibration sensing performance studies are conducted. The results demonstrate that the proposed sensor exhibits a resonant frequency of 175 Hz, a flat frequency response in the range of 10~100 Hz with a high vibration acceleration sensitivity of 57 pm/m/s². Additionally, the sensitivity of the sensor cross axis is only 4.2% of that in the vibration direction, indicating that the sensor has strong resistance to transverse interference. The FBG vibration sensor proposed in this paper possesses high detection sensitivity and a wide operating frequency band, which can serve as a reference for high-precision detection of low-frequency vibration signals in engineering applications.