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A fiber Bragg grating (FBG) accelerometer based on double diaphragms is presented and experimentally demonstrated. Design, fabrication, and optimization of the FBG accelerometer are analyzed. Experimental results indicate that the FBG accelerometer provides broad flat frequency range from 50 to 800 Hz, corresponding sensitivity range from 23.8 to 45.9 pm/G, while the flatness is <;3 dB. Cross-axis sensitivity is <;2.1% of the main-axis sensitivity, dynamic resolution can reach 0.385 mG/√(Hz), and dynamic range is 80 dB. Random error of the FBG accelerometer is analyzed by using Allan variance analysis method, which is promising in cross well seismic exploration.