In the process of deep oil and gas exploration,low-frequency signal plays a key role. Therefore, accelerometers that can receive low-frequency signals are particularly important in low-frequency exploration. Compared with electric accelerometers, the Fiber Bragg Grating (FBG) accelerometer has the characteristics of anti-electromagnetic interference, small size, high-temperature resistance, and high resolution. Researchers have proposed various FBG vibration sensor structures, in which cantilever beam and circular diaphragm are two typical structures and have been widely studied. The early single cantilever fiber grating sensor has the characteristics of high sensitivity and weak lateral interference resistance. In contrast, the ordinary circular diaphragm structure has strong lateral interference resistance and low sensitivity. In this paper, we propose a low-frequency FBG accelerometer based on a diaphragm-type cantilever structure. It combines a plane circular diaphragm and an equal strength cantilever beam into one, which reduces the lateral interference and enhances the sensitivity coefficient. The diaphragm-type cantilever is made of a beryllium bronze sheet into a circular diaphragm. Then four symmetrically distributed equal strength cantilever beams are cut into the diaphragm. The four suspension beams jointly support a copper inertial mass block located in the diaphragm center. The edge of the diaphragm is fixed between the base and the gasket through screws. An FBG with a central wavelength of 1 539.15 nm, a reflectivity of 90% and a grating area length of 10 mm is selected. The FBG is pasted at two points and fixed on the centerline of one cantilever of the diaphragm-type cantilever with 302 glue. The tail fiber at one end passes through the gap between the diaphragm-type cantilever and the gasket and is connected with the external optical demodulation equipment. According to the theoretical analysis, the optimal size of structural parameters of the diaphragm cantilever beam is obtained by MATLAB numerical simulation. According to the optimal size, a finite element model is established by COMSOL simulation software to further analyze the vibration form of the structure. The simulation results show that when the edge of the diaphragm cantilever is set as a fixed constraint, the resonance frequency of the first mode is 49.5 Hz. The vibration form is that the central mass of four cantilever supports vibrates up and down along the z-axis, and the vibration mode conforms to the original design intention. Simultaneously, the tested results of sensing characteristics from the shaking table indicate that the system has an excellent response to low-frequency acceleration excitation signals when the natural frequency of the system is 48 Hz. The frequency response range of the system is 1~35 Hz, in which the acceleration sensitivity is 452.6 pm/g. The acceleration sensor is designed with strong lateral immunity since the sensitivity in the transverse sensitivity is only 2.16% of the sensitivity in the working direction. Therefore, the designed FBG accelerometer provides a new method for the single component FBG accelerometer in the practical application of seismic exploration.