A highly sensitive fiber-optic vibration sensor is developed based on the Pound-Drever-Hall (PDH) frequency locking scheme of a fiber Bragg grating (FBG) Fabry-Perot (F-P) cavity. It measures the vibration signal by the error signal transferred and amplified from the phase change of the F-P cavity. The sensor system exhibits experimentally a nice sensing capability to the vibration signals within a frequency range from 1 to 5 kHz and it can obtain a more than 50dB signal to noise ratio. The analysis of the sensor, taking into account the parameters of elements used in the system and many environment factors, shows that it may reach a resolution as high as 11.7×10-12 strain/Hz, which is much better than those of the traditional fiber sensing systems.