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A novel optical fiber pressure sensor based on Fabry-Perot (FP) interferometer and phase demodulation method is described. MEMS techniques and the common communicational components are used to fabricate the sensor. The principles of pressure measurement and sensor design have been introduced. Phase demodulation method based on Fourier transformation is explored, which can reduce errors resulting from intensity variation of light source. Experimental results demonstrate that the sensor has reasonable linearity, sensitivity and a wide pressure measurement range from 0.1MPa to 3MPa.