A scheme of long-distance fiber Bragg grating (FBG) sensor system based on linear-cavity fiber Raman laser is proposed and demonstrated. The cavity of the laser consists of the sensing FBG and the tunable FBG, of which the Bragg period is tunable through a one-dimensional (1D) adjustor. The 1D adjustor, which is connected with a step motor that is controlled by a programmable logic controller (PLC), can control the Bragg period of the tunable FBG to match the Bragg period of the sensors, which decide the wavelength of the laser output. The tuning module, the optical/electrical circuit, the detecting-and-controlling system and the fiber Raman laser construct a close loop, which performs the wavelength demodulation. Experimental results show that the demodulation sensor system can accomplish sensing and detecting of long-distance distributed sensing signal. Signal-to-noise ratio of stable Raman laser output is greater than 40 dB with 30 km non-zero dispersion shifted fiber (NZDSF), and the precision of the proposed system is about 0.05 nm in a demodulation range of 4.2 nm.