In this paper, a variable inertance and variable damping (VIVD) vibration control system with an electric circuit is proposed and analysed. By connecting a VD device and an inerter in series, a VI device can be composed, which can vary its equivalent inertance by controlling the damping of the VD device. A single degree of freedom suspension with the VI and VD capabilities are analysed in the frequency domain. The result shows that the VIVD semi-active system can have much better vibration control performance than the conventional VD system. The VIVD system is complicated to implement with mechanical networks. Hence, based on the mechanical-electrical analogies, the mechanical energy is transferred to electrical energy with an electromagnetic damper, and then an electric circuit is designed to simulate the VIVD device. The frequency and time domain analyses both validate the correction of design. The VIVD vibration control system can significantly improve the semi-active system's performance.