Based on the analysis of matched grating demodulation principle, a novel fiber Bragg grating (FBG) vibration sensor was designed. A simply supported beam structure is adopted, so center wavelength of sensing grating and natural frequency of the sensor can be changed by adjusting the beam. The matching demodulation is achieved. At the same time, the range of frequency measurement is expanded. The sensor has good frequency detection performance in standard signal vibration detecting experiments. The frequency scope is up to 200 Hz. In addition, the detected signal has good signal to noise ratio at 20 Hz and 190 Hz.