A　measurement　of　the　leakage　position　in　a　distributed　optical　fiber　acoustic　sensor　system　based　on　Sagnac　interferometer　is　demonstrated.　The　effect　of　the　input　polarization　on　the　output　power　of　the　demodulated　signal　is　researched　theoretically　and　experimentally.　The　influence　of　the　polarization　of　the　signal　and　the　reference　on　the　measurement　sensitivity　is　calculated.　Theoretical　analysis　and　experimental　simulation　are　carried　out.　The　results　show　that,　when　the　system　is　10.044　km　long,　the　least　frequency　measured　is　20　kHz　and　the　calculated　leakage　position　is　5　km,　which　is　close　to　the　real　leakage　position　of　5.022　km.　The　relative　difference　is　0.44%.