A rapid-cycling superconducting magnet is currently under development for the next-generation heavy-ion therapy. The non-oriented electrical steel (NOES) sheet, M470-50A5, is adopted as the cold iron yoke in the superconducting magnet to enhance the field and minimize the AC losses. In this paper, we measure the magnetic properties, magnetic permeability and hysteresis loss of a 0.5-mm thick NOES sheet at 4.2 K, 77 K and room temperature with a toroidal test specimen. The magnetic permeability as well as the hysteresis loops are investigated with a very low frequency until 3 T. To provide the magnetization for the magnet design, we modify the Jiles–Atherton (J–A) model so that the modified J–A model can predict not only the magnetization loops but also the magnetic permeability until a high magnetic field region.