This paper discusses an applicable fiber-optic accelerometer composed of a transmissive grating panel, a reflection mirror, and two optical fibers with a separation of quarter grating pitch as transceivers that monitor the low-frequency accelerations of civil engineering structures. This sensor structure brings together the advantages of both a simple sensor structure, which leads to simplified cable design by 50% in comparison with the conventional transmission-type fiber optic accelerometer, and a stable reflected signals acquisition with repeatability in comparison to the researched grating-reflection type fiber optic accelerometer. The vibrating displacement and sinusoidal acceleration measured from the proposed fiber optic sensor demonstrated good agreement with those of a commercial laser displacement sensor and a MEMS accelerometer without electromagnetic interference. The developed fiber optic accelerometer can be used in frequency ranges below 4.0 Hz with a margin of error that is less than 5% and a high sensitivity of 5.06 rad/(m/s)(2).