There is a demand for simultaneous measurement of static absolute signal and dynamic relative signal with optical fiber sensor in many situations, which requires the sensing system has both large dynamic range and high accuracy. White light extrinsic Fabry- Perot interferometric (EFPI) sensor system based on fast light spectrum acquisition is utilized to meet the requirement of large dynamic range and absolute measurement,which can also response dynamic signal rapidly. Zoom-FFT algorithm is applied in cavity length demodulation of sensors to improve the demodulation accuracy, and the experiment shows that the accuracy reaches 4 nm. Zoom-FFT algorithm can satisfy the demand for demodulation speed of dynamic measurement because of its low computation cost. The experiment is conducted to calibrate the sensor in liquid level between 0~30 cm, which shows that the response of the sensor has a desirable linearity to the static pressure, and the liquid level resolution reaches 0.13 mm. One sensor is able to measure liquid level depth and sound simultaneously with the difference between the frequencies of them at the same time. And the proposed system is proved to possess the potential application in simultaneously absolute measurement of static signal and relative measurement of dynamic signal.