According to the perturbation theory, the coupled-mode equations for guided optical waves in the magneto-optical fiber Bragg gratings (MFBGs) under non-uniform magnetic field are derived. The equivalent relation between the magneticallyinduced non-uniform fiber Bragg grating (MnFBG) and the corresponding non-magnetic chirped grating is expressed and verified by the piecewise-uniform MFBG model under linear magnetic field. On the basis of the equivalent relation, the MnFBGs can be effectively investigated by means of simulations. The characteristics of the MnFBGs under three typical magnetic field distributions with application to optical pulse compression are simulated, and the minimal pulse width can be achieved for the same magneto-optical coupling parameter of 2.2 × 103 m-1. The equivalent relation between the magnetically induced non-uniform fiber Bragg grating (MnFBG) and the corresponding non-magnetic chirped grating is expressed and verified by the piecewise-uniform MFBG model under linear magnetic field. On the basis of the equivalent relation, the MnFBGs can be investigated by means of simulations. The characteristics of the MnFBGs under three typical magnetic field distributions with application to optical pulse compression are simulated, and the minimal pulse width can be achieved for the same magneto-optical coupling parameter of 2.2 × 10 3 m -1.