According to the perturbation theory for guided optical waves, coupled-mode equations in linearly birefringent magneto-optic fiber Bragg gratings (LB-MFBGs) as well as its analytical solution are presented. Dependence of optical polarization state in the LB-MFBGs on linear birefringence and magnetically circular birefringence is in detail investigated by means of normalized Stokes parameters. It is shown that, in the LB-MFBGs there exist two eigenstates of polarization (left-handed and right-handed elliptically polarized light), and the birefringence effects only change the ellipticity, instead of the azimuth of principal axis. By changing the relative magnitude of the linear and circular birefringence, the output polarization states could be controlled, which is helpful for the potential applications of the LB-MFBGs in optical fiber communication and sensing.