Distributed fiber acoustic sensing based on coherent optical time-domain reflectometry (C-OTDR) is an important tool for vibration detection. However, the response of the C-OTDR system is affected by the intensity fluctuation of the interfering light, which makes quantitative measurement difficult. The response characteristics of a commercial C-OTDR system in the typical case of a single-frequency continuous point vibration source are studied. Experimental results show that the system can detect the location and the central frequency of the vibration accurately. And two signal processing methods are examined. The linear relation between the response and the excitation amplitude can be restored through averaging the spectra in time domain. The distribution of vibration amplitudes is maintained by the spatial distribution of the response within a certain range. The two methods can negate the influence from the signal fluctuation satisfactorily, which is helpful to realize more consistent and precise measurement of the system.