An optical fiber vibration sensor based on a core-offset structure is proposed and demonstrated. This kind of fiber sensor shows a nice comb filter property and has a high extinction ratio. The curvature sensing characteristic of the core-offset structure is analyzed. The experiment results show that this kind of sensor exhibits a linear response to bending curvature. The vibration characteristic of the sensor is studied at this basic. And the vibration responses of the sensor with the input laser wavelengths located in the linear responding area and in the transmission peaks or dips are analyzed. The results show that this kind of vibration sensor exhibits a fine vibration response with the input laser wavelength located in the linear responding area, just like Mach-Zehnder fiber interferometer. In addition, the sensor shows a nice noise characteristic when there is no vibration, which means good application prospects.