Random residual circular birefringence induced by a twist of single-mode fiber is the main cause of magnetic field Faraday phase error in depolarized interferometric fiber optic gyroscopes (D-IFOGs). Magnetic field Faraday phase error in D-IFOG includes both radial and axial phase errors; however, axial phase error has not been thoroughly researched and is usually neglected. A magnetic phase error model of D-IFOG along a radial direction is established by using a Jones matrix; then, the mathematical description of radial direction phase drift in D-IFOG is deduced according to the model. Based on a quadrupolar winding distribution structure in a fiber loop, a magnetic phase error model of D-IFOG along the axial direction is established, and phase drift in D-IFOG is deduced by using a coil expansion method. Theoretical analysis shows that nonreciprocal phase error in D-IFOG induced by magnetic field correlates with several factors, such as optical coherent length, optical polarization degree, etc. Then, measures to restrain the magnetic field phase error in D-IFOG are investigated, such as the new Lyot depolarizer, electromagnetic shielding, etc. Further, we experimentally present the performance of D-IFOG with the magnetic intensity of 150 Gs along axial and radial directions, respectively, and verify the effect of a new Lyot depolarizer on restraining magnetic phase error in D-IFOG.