We present a highly sensitive fiber Bragg grating (FBG) based microphone with a flat response and static pressure equalization. A very high dynamic sensitivity is achieved by a pressure sensing structure based on a carbon fiber diaphragm. Static pressure equalization is realized by a balance structure with a capillary glass tube. The resonances of the sensor are suppressed by air damping structures, and a broadened flat response is achieved. Acoustic-solid interaction model was used to analyze the response characteristics of the microphone. A sensor prototype was produced and tested, and the results are well consistent with the design. The tested sensitivity was -10 dB re 1 pm/Pa from 10 Hz to 2.5 kHz, with a fluctuation of less than ±1.5 dB. Combined with the PGC (Phase Generated Carrier)-based coherent detection scheme, the microphone can achieve a sound resolution of mPa level. The static pressure sensitivity is measured to be -0.27 pm/atm, which is 100 dB lower than the dynamic sensitivity.