A novel structure of fiber-optic Sagnac sensor, which could eliminate dead zone, was proposed. The optical path circulation was realized by a 2×2 coupler. The optical path was analyzed based on Jones matrix. If the length of delay loop was selected properly, the dead zone of the sensing optic-fiber could be eliminated and the disturbance of false zero frequency could be filtered. After filtering and smoothing, the signal, acquired at eight different points, was fitted by least-square method and the zero frequency was obtained. According to the experimental results, the source of disturbance was located with maximum error 68m and minimum error 3m .The validity of the structure was testified, which indicates that the structure could be used to monitor the leakage at long distance pipeline.