The principle of the in-line Sagnac interferometer current transducer is introduced. The Sagnac fiber-optic current sensor is deeply researched, and the complete system theory model has been established. The factors which affect the measuring precision are comprehensivelly analyzed and simulated. Some rules which influence the system precision are acquired. The polarization errors of the in-line Sagnac interferometer current transducer are studied by using the Jones matrices formalism. The effects of linear and cirular birefringence in the sensing coil on measuring precison are simulated, and curves and typical error data which represent the effecting rules are theoretically acquired. The simulation result shows that the linear birefringence can be restrained by adding a larger amount of circular birefringence in the sensing fiber.