The magnetic properties of highly grain-oriented electrical steel vary along different directions. In order to investigate these prop-erties, standard Epstein samples were cut at different angles to the rolling direction. The hard magnetization direction was found at an angle of 60° to the rolling direction. To compare the measured and fitting curves, when the magnetic field intensity is higher than 7000 A/m, it is appropriate to simulate the relation of magnetic permeability and magnetization angle using the conventional elliptical model. When the magnetic field intensity is less than 3000 A/m, parabolic fitting models should be used; but when the magnetic field intensity is between 3000 and 7000 A/m, hybrid models with high accuracy, as proposed in this paper, should be applied. Piecewise relation models of magnetic per-meability and magnetization angle are significant for improving the accuracy of electromagnetic engineering calculations of electrical steel, and these new models could be applied in further industrial applications.