This paper investigates the lag time and the highest working frequency of Fiber Bragg Grating strain sensor in which strain wave transfers to bare FBG by analyzing the transmit course of the strain wave. The results show that the FBG strain sensor is applicable to the measurement of low frequency vibration in engineering. As its application, FBG strain sensors are used in the shake table test of offshore platform model and show good capability in measuring the dynamic strain of vibration system with low frequency.