Aiming at the problem that the optical fiber vibration acceleration sensor is influenced by temperature and its sensitivity is low, an optical fiber vibration measurement system with temperature compensation function was designed. The ambient temperature, which is used to compensate for the vibration acceleration to reduce the effect of temperature on the vibration measurement, was measured by a fiber Bragg grating. The tunable Fabry-Perot filter was used for wavelength demodulation and also as the fiber mirror to improve the sensitivity of the sensor. The mutual influences of vibration measurement and temperature measurement were analyzed and tested, the results show that the effect of the Fabry-Perot filter scanning on vibration measurement can be eliminated by data processing and the influence of vibration on temperature measurement is small.The temperature stability and sensitivity of the system were tested by experiments, which show that the maximum relative error of the vibration acceleration measurement is 1.65% under the temperature range of 25℃ and the sensitivity of vibration measurement is 107.70 mV/g.