A combined algorithm of minimum mean square error estimation and Fibonacci method for fiber Fabry-Perot interferometer was proposed. This united algorithm uses the Fibonacci method to quickly search a series of cavity length estimators and finds the one as demodulation gap which corresponds to the minimum mean square error value. The relationship between iteration number and demodulation accuracy was analyzed by simulation, and a temperature measurement experiment was carried out. The results show that, the average error of this algorithm is less than 2×10－5 pm theoretically, linear fit of actual cavity length is above 0.999 9, and dynamic range is up to 2.5 mm. In the experiment, the resolution of algorithm is 0.15 nm, corresponding to a temperature resolution of 0.03℃ with quick demodulation time 0.03 s, both high resolution and fast demodulation speed can be achieved.