We present a high-sensitivity fiber Bragg grating (FBG)-based microphone with a flat response and static pressure equalization. A very high dynamic sensitivity of the microphone 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. An acoustic-solid interaction model was used to analyze the response characteristics of the microphone. An experimental 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 phase-generated-carrier-based coherent detection scheme, the microphone can achieve a sound resolution of the milli-pascal level. The static pressure sensitivity is measured to be 0.27 pm/atm, which is 100 dB lower than the dynamic sensitivity.