In order to meet the requirements of high accuracy and rapid measurement of seawater temperature, we propose a temperature sensing scheme based on optical fiber Farby-Perot (F-P) sensor. The sensor is composed of silicon chip and fiber tail, and the silicon chip acts as the F-P cavity of the optical fiber F-P sensor. Temperature sensing is realized based on the thermal optical effect and thermal expansion effect of silicon. The demodulation algorithm of optical fiber F-P sensor is the fast cross correlation demodulation algorithm based on dichotomy, which can realize high precision and fast demodulation. The experimental results of optical fiber F-P temperature sensor show that the sensor can reach the precision of 0.15 ℃ and distinguish the temperature change at 0.001 ℃, and the temperature response time can reach 128 ms. The sensor is expected to be applied in the field of disposable measurement.