We have demonstrated a novel Fiber Bragg Grating sensing system based on a Fabry-Perot tunable filter for measuring dynamic processes. This system is very suitable for multipoint vibration or dynamic strain detection. However, in some conditions, the response time of Fabry-Perot tunable filter will influence the sensitivity of the sensor that the sensitivity is not kept constant. Therefore, post-processing for the measured vibration signal is necessary to solve this problem. In this paper, the demodulation technique of this system is briefly described and two signal processing methods are introduced to deal with the measured signal to obtain stable measurement of the vibration/dynamic strain over the response time of Fabry-Perot tunable filter. In the experiment, program controlled multipoint dynamic strain detection is successfully implemented by this system with these signal processing methods.