According to the coupled-mode perturbation theory, the coupled-mode equations for spun magnetically-induced fiber Bragg gratings (SMFBG) is derived. The dependency of grating spectra on the spun-induced refractive index change is numerically analyzed by using the shooting method and the theoretical results are identical with the experimental data from literatures. The concept of magnetically-induced circular-polarization dependent loss (MCDL) is proposed for analyzing the magnetic field sensitivity of SMFBG. It is shown that the MCDL of high-speed spun (or isotropic) SMFBG possesses optimal magnetic field sensitivity; however, the appropriately low-speed spun MFBG has a larger peak MCDL, which is helpful to magnetic measurement. Compared with the polarization-dependent loss (PDL) method, the MCDL method is less dependent on linear birefringence and is more convenient for theoretical analyses.