The transmission characteristics of magneto-optic fiber Bragg grating(MFBG)-based Fabry-Perot(FP) structures dependent on the magneto-optical effect and the initial phase of effective refractive index distribution of gratings are analyzed by the transfer matrix method. By adjusting the applied magnetic field, the function of tunable filtering for MFBG-FP structures is implemented and the magnetic control of transmission peaks is also useful for eliminating the influence of the initial index phase difference. For the case of high reflectivity of gratings, the position and wavelength spacing of transmission peaks can be analytically expressed by the effective cavity length and the effective magneto-optic coupling coefficient. The magnetic tunability of MFBG-FP is enhanced with the increase of the ratio of FP cavity to MFBG magneto-optic coupling coefficients. When the ratio is more than 1, the MFBG-FP has an advantage over the corresponding MFBG in magnetic tuning.