This article proposes a novel semiactive electromagnetic device with the capability of variable inertance and damping (VIVD) and an energy storage priority control (ESPC) strategy for vibration reduction of vehicle seat suspensions. The VIVD device can control its inertance and damping by adjusting resistances in a variable admittance (VA) circuit different from the traditional mechanical damper. The circuit and mechanical dynamics model of the VIVD seat suspension is analyzed and verified with tests, and the energy storage characteristic and controllability of the VIVD device are explored. Also, the frequency response characteristics of the VIVD device are derived from the admittance characteristics of the VA circuit. For the semiactive VIVD seat suspension, an H∞ controller is designed to obtain the desired control force. An ESPC strategy is proposed to make the electromagnetic force of the VIVD device track the desired control force. The test results show that the VIVD seat suspension can successfully suppress the seat's vibration, which is better than the traditional variable damping seat suspension performance. Under the random excitation, the root means square acceleration of the VIVD seat is reduced by 32.99% compared with a passive seat. This new semiactive VIVD device shows great potential in engineering applications.