A theoretical analysis of the magneto-photorefractive effect for different holographic recording configurations in LiNbO3:Fe is presented. All of the magneto-photovoltaic tensor elements are tabulated. And the equations of the bulk photovoltaic and the magneto-photovoltaic current for four different holographic recording configurations are given. Our results show that the diffraction efficiency of holographic grating depends on the applied magnetic field for each configuration, since the magneto-photorefractive effect induces a change in the electric current. For different configurations, the influence of the nonlinear effect in LiNbO3:Fe induced by the magnetic field is different. A method for measuring certain tensor elements is discussed.