This paper proposes a new electrically controlled magnetic variable-speed gearing (EC-MVSG) machine, which is capable of providing controllable gear ratios for hybrid electric vehicle (HEV) applications. The key design feature involves the adoption of a magnetic gearing structure and acceptance of the memory machine flux-mnemonic concept. Hence, the proposed machine can not only offer a gear-shifting mechanism for torque and speed transmission, but also provide variable gear ratios for torque and speed variation. The electromagnetic design is studied and discussed. The finite-element method is developed with the hysteresis model to verify the validity of the machine design.