A measurement of the leakage position using a distributed optical fiber acoustic sensor system based on Sagnac interferometer was demonstrated here. The effect of the input polarization on the output power of the demodulated signal was researched theoretically and experimentally. The influence of the polarization of the signal and the reference on the measurement sensitivity was calculated. It is shown that a higher coherence between them could obtain a higher measurement sensitive result; uprightness between them could not obtain any leakage signal. There are theoretical analyses and experimental simulation in this paper. When the system is 10.044km-long, the least frequency measured was 20 kHz and the calculated leakage position was 5-km, which was close to the real leakage position 5.022km. The relative difference was 0.44%.