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Tunable laser is one of the most important components in the fiber Bragg grating demodulation system.The stability of its output wavelength and power affects the performance of the whole demodulation system. In this paper, the tuning principle of MG-Y tunable laser is analyzed, and a tunable laser control circuit based on FPGA is designed. The circuit uses a temperature control chip ADN8834 to control the temperature of the MG-Y laser, and controls output wavelength of the laser by changing the output current of the current source. The output wavelength of the laser is analyzed by spectrum analyzer, and the output wavelength of laser is calibrated, and the wavelength-current query table is made. The wavelength of the laser can be scanned continuously in the range of 1527 ~ 1567 nm at the interval of 20 pm by FPGA calling the wavelength-current query table. At the same time,a fiber Bragg grating demodulation system was built to verify the feasibility of the tunable laser to demodulate the center wavelength of the fiber grating.