In this article, a fiber optic accelerometer based on a Fabry-Perot interferometer is presented and prepared by micromachining on a silicon substrate. The inertial sensing structure of the accelerometer is built by a center block mass and four folded springs with a high thickness-to-width ratio, providing an in-plane resonance vibration. The miniature-sized sensor has large flexibility in structural design and its acceleration response can be predicted by theoretical estimation and finite element simulation. Experimental results show that the proposed sensor's sensitivity is over 161 rad/g in frequency range of 1 to 63 Hz. It also achieved a low average noise level of 67.4 ng/Hz1/2 on the working band. The sensor's transverse crosstalk is less than 1.38%, proving its potential ability in low frequency vibration detection applications.