Fiber Bragg gratings have has been widely used in sensors. We analyze the transmission and polarization properties of magneto-optical fiber Bragg gratings based on coordinate conversion. The simulations demonstrate the influence of magnetic field intensity on the transmission spectrum, the polarization properties by the coupled mode theory, and the Jones formalism. The results show that while a small magnetic field can hardly be detected in the grating amplitude response, it leads to significant polarization properties such as the third normalized Stokes parameter, polarization dependent loss, and ellipticity. We demonstrate that these polarization properties contain information about the magnetic field and can thus be used for magnetic field sensing purposes. The sensitivity and dynamic range depend on the physical parameters of the grating.