The characteristics of a fiber-optic Fabry–Perot interferometric acoustic sensor are investigated. An improved phase-generator carrier-demodulation mechanism is proposed for obtaining a high harmonic suppression ratio and stability of the demodulation results. A gold-coated polyethylene terephthalate membrane is used as the sensing diaphragm. By optimizing the parameters and the demodulation algorithm, the signal-to-noise ratio (SNR) and distortion ratio of 50.3 dB and the total harmonic distortion of 0.1% at 114 dB sound pressure level (SPL) (@ 1 kHz) are achieved, respectively. The sensor shows good temperature stability; the variation of the response is within 0.6 dB as the temperature changes from −10°C to 50°C. A sensitivity of 40 mV/Pa at 1 kHz and a frequency response range of 100 Hz to 12.5 kHz are reached, respectively. The SNR of the system is 60 dB (Re. 94 dB SPL). The sensor may be applied to photoacoustic spectrometers as a high-performance acoustic sensor.