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We propose a novel fiber Bragg grating (FBG) sensor system using a linear-cavity fiber laser scheme with a distributed Raman amplifier as a gain medium. The inhomogeneous broadening property of the distributed Raman amplifier is used for multiwavelength operation. The experiment shows that such a linear-cavity fiber Raman laser can provide a stable output with an optical signal-to-noise ratio over 50 dB even if the FBG is located at a 25-km remote sensing position. The feature of our proposed fiber laser can facilitate a long-distance or a large-scale fiber sensor system and can be easily extended for multipoint sensing applications.