The methods of sensor and demodulation with matched fiber Bragg gratings (FBG) used as direct light intensity elements in vibration sensor are introduced. The expressions of reflection and transmission spectra of FBG are deduced, which provides a qualitative explanation of sensor mechanism. Then mathematical models are established in order to make simulation. The method can perform single point demodulation with matched FBG and can turn the sensor signals into intensity variation of the output of FBG. The experimental results are in excellent agreement with the theory, which proves the feasibility of this method.