As the main transportation facilities, such as petroleum, natural gas, city water, and among others, the pipeline has been concerned extensively for its safety in operation. Meanwhile, to find and locate the positions of the persistent small-scale leakage of the pipeline is one of the major issues and difficulties faced by the safe operation of the pipeline. When Sagnac fiber interferometer is in the use of monitoring and positioning of a small leak on pipeline, the interference result of the two coherent laser beams in Sagnac ring will be affected by the random change of light polarization, thereby affecting the interferometer performance of linear Sagnac fiber optic interferometer. A new method is proposed to suppress the influence of random change of polarization on Sagnac interferometer. By modifying the structure of interferometer, an optical depolarizer is introduced into the Sagnac ring to improve the operational stability. Experimental results show that this method is a good solution to solve the deterioration of sensitivity caused by polarization fading.