A Twice-FFT demodulation method for signal distortion state is proposed and experimentally demonstrated in an optical fiber Fabry-Perot (FP) acoustic sensor. Here the fiber FP acoustic sensor element is build with fiber end face and combination of diaphragms which is composed of a small round aluminum foil and a polymer PET film. The hypotenuse intensity demodulation method is applied to acquire the acoustic signal in time domain assisted with a Photodetector (PD) and an oscilloscope. The first Fast Fourier transform (FFT) processing results show harmonic distortion on the frequency domain spectrum. To demodulate the acoustic frequency and amplitude information, twice-FFT processing is preformed. Experimental results reveal an accuracy up to 95.6% of acoustic signal in the frequency range 2-100 Hz. Our scheme provides a new option for signal demodulation of optical fiber acoustic sensors (OFAS).