Fiber Bragg grating (FBG)-based accelerometer has been a research focus in the fields such as civil, electromechanical and aerospace. The principle and mechanical model of FBG-based accelerometer are introduced briefly. The latest development of FBG accelerometers with different structures and principles is emphasized. According to different operating frequency ranges, the present situation of the development of FBG accelerometer with low and high resonant frequencies is expounded respectively. Particularly, this paper illustrates the accelerometer capable of acceleration measurement in multiple dimensions simultaneously. And the further outlook of FBG accelerometer is prospected.