The Fiber Bragg Grating (FBG) vibration sensor based on the cantilever beam structure has strong lateral anti-interference ability, high stability, and simple structure. It is particularly suitable for one-dimensional acceleration measurement. And its working range and resolution are determined by its resonant frequency and sensitivity, however, because the resonant frequency and sensitivity of cantilever beam type sensors are mutually restricted, it is difficult for the current generation of cantilever beam type sensors to simultaneously meet the requirements of wide measurement bandwidth and high sensitivity. To satisfy this demand, a novel FBG accelerometer based on F-beam is developed. The FBG can be sensitized by the neutral layer far away from the cantilever beam, and suspended and fastened at both ends to successfully prevent the chirp effect of FBG.Firstly, the amplitude-frequency characteristics of the damped mass-spring system with one degree of freedom are studied. The flatness of the amplitude-frequency response curve varies with the change of the damping ratio. Without damping, the sensor's working bandwidth is narrow. By adding damping materials such as silicone oil, the sensor can have a larger working bandwidth. Generally, the damping ratio is 0.7. After that, the resonant frequency and sensitivity formulas of the sensor are derived, and its mathematical model is established according to these formulas. With the sensitivity formula as the objective function, and its size parameters and the resonant frequency formula as the constraint conditions, the sequential quadratic programming program is established by MATLAB to optimize the solution, and the sensor's size parameters that satisfy the operating band range and have high sensitivity are obtained. Imported 3D model of this sensor created by SOLIDWORKS into ANSYS software, where the material properties are adjusted, the mesh division is finished, and fixed constraints are given to the sensor base to produce the sensor's first-order and third-order modal vibration patterns. The modal analysis results verify the correctness of the theoretical analysis and show that the sensor has a good transverse anti-interference ability. And then, set the simulation conditions such as sweep frequency range to analyze the harmonic response of the sensor. By modifying the damping ratio, the simulated amplitude-frequency response curves under the conditions of two damping ratios are obtained to simulate the amplitude-frequency response of the sensor without silicone oil and filled with silicone oil. The simulated amplitude-frequency response curve at the maximum amplitude position is basically consistent with the theoretical curve. Finally, based on the theoretical and simulation results, two sensors were fabricated, one of which was directly encapsulated as sensor 1 and the other was encapsulated with silicone oil as sensor 2, and the amplitude and frequency response tests, sensitivity tests and transverse immunity tests were conducted on sensor 1 and sensor 2. In order to determine the sensor's amplitude-frequency response, the trigger signal's amplitude is fixed swept between 10 Hz and 240 Hz. Next, the sensor's minimum detection frequency is tested by continuously varying the excitation frequency between 0 Hz and 2 Hz, and the detection performance of the sensor under various excitation conditions is tested by setting various excitation conditions. In the sensitivity test experiment, fixed the excitation frequency and adjusted the acceleration to measure the sensor's sensitivity. In the lateral immunity test experiment, fixed the excitation frequency and acceleration, change the measurement direction to test the sensor's lateral immunity.The experimental indicates that the experimental results of sensor 1 and sensor 2 are basically consistent with the theoretical and the simulated amplitude-frequency curve. The resonant frequency of sensor 1 is about 168 Hz, the measurement bandwidth is 1.5~50 Hz, the sensitivity coefficient is 159.84 pm/g, the transverse immunity is 9.88%, and the error between the theoretical and actual values of resonant frequency and sensitivity is 0.93% and 3.29% respectively. The error may be caused by the low processing accuracy of the sensor in the production process and the immature fiber pre-stretching process. The measurement bandwidth of sensor 2 filled with silicone oil is 1.5~100 Hz, the sensitivity coefficient is 133.57 pm/g, and the lateral interference immunity is 8.1%. This two FBG sensors can well reflect the external sinusoidal excitation in their corresponding operating bands and have good detection performance. By filling silicone oil, the working frequency band can be effectively expanded, the sensitivity can be stabilized, the transverse interference immunity can be improved, and the measurement error can be reduced.