A compact fiber Bragg grating (FBG) accelerometer is proposed and investigated in this paper. The sensor is designed to consist of an L-shaped beam structure, an inertial mass and an FBG. The vibration displacement of the mass can be effectively converted into the axial strain of the FBG to realize acceleration measurement through this structure. The natural frequency and sensitivity of the sensor are theoretically analyzed, which largely determine the performance of the sensor. Then, the sensing characteristics of the sensor are tested and verified by some experiments. The research results show that the amplitude-frequency response of the sensor is flat in the frequency range of 50~200 Hz, and the measured natural frequency of the sensor is about 275 Hz. The wavelength of FBG has a good linear response to external acceleration, the average sensitivity is about 54 pm/g, and the linearity is greater than 99.8%. The temperature experimental results show that the sensor has a relatively stable response to ambient temperature, the average temperature sensitivity is low at about 11.5 pm/oC in the range of 27 oC~80 oC, and the heating curve and the cooling curve are in good agreement. The sensor proposed in this paper owns the merits of small size, light weight, compact structure, convenient installation and low cost, and can be applied to medium-low frequency acceleration measurement.