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A displacement sensor with subnanometer resolution based on the fiber-optic Fabry-Perot interferometer is proposed. The Fabry-Perot cavity is formed between the fiber end face and a high reflectivity mirror, which effectively improved the contrast of the interference fringe. Meanwhile, since the measuring range and the demodulate resolution for Fabry-Perot sensor are difficult to be improved simultaneously, a novel demodulation method based on the combination of the Fourier transform method and the minimum mean square error estimation-based signal processing method has been presented, which is capable of providing subnanometer resolution and absolute measurement over a wide dynamic range. The experimental results show that the resolution of the sensor is up to 0.084 nm over a dynamic range of 3 mm.