A fiber-optic accelerometer based on extrinsic Fabry-Perot interferometer (EFPI) is reported. The sensor adopts flywheel diaphragm structure as a sensitive element, where the mass block is bonded in the center, while the beam of the flywheel acts as a spring. The sensitive element forms single degree of freedom spring-mass-damper system. The parameters of the accelerometer are designed based on finite element simulation (FEM), and the transfer function of the sensor is established by numerical simulation. The experiments indicate that the sensor has a wide detection frequency band with the detectable ability for micro-vibration low as 0.01 Hz, and the sensitivity is 7.02 rad/g @20 Hz, and reach an average sensitivity of 6.39 rad/g in 5-20 Hz. The research shows that the accelerometer has a good development prospect in the field of low frequency micro-vibration detection.