The performance of the fiber optic current sensors (FOCSs) is limited by the linear birefringence (LB). Faraday mirror can be employed to compensate the LB by exploiting the non-reciprocity of Faraday effect and the reciprocity of LB. In this paper, the structure and principle of the FOCS using Faraday mirror are addressed, and the simulated results showing the influence of LB on FOCS are presented. The results indicate that the influence of LB disappears when the current is null. However, when the current is not zero, the LB is not removed and the extent of effect is different with different LB. Considering the LB is not easy to remove, a method to directly measure Faraday rotation in the presence of LB by time multiplexing of three different states of polarization is proposed. The Faraday rotation can be deduced directly from the detected signals and the LB need not be compensated physically by employing this technique.