Dynamic Voltage Restorer (DVR) is one of the most cost-effective equipment to mitigate voltage sag, which has been widely used. However, the application of DVR also inevitably influences the stability of the interconnected system. To analyze the stability problems that DVR brings to the inter-connected system, it is necessary to study the impedance characteristics of the DVR. In this paper, an impedance model of the single-phase DVR is established based on the linear model of the single-phase DVR in detail; then, the stability criterion of the single-phase interconnected system with DVR is deduced using the impedance model of DVR. Simulation results indicate that the impedance model, as well as the stability criterion, is applicable in a wide frequency band.