This paper proposes a novel wound-rotor machine which has a single-phase stator winding and three-phase rotor windings. The machine is called Single-Phase Wound-rotor Machine (SPWM). The machine can be driven in motoring and generating modes in single-phase grid system. The dynamic model and control system of the machine are also designed. Typically, the double revolving field model is used for singlephase machines, but it includes only the steady-state characteristics. So, the double revolving voltage model was proposed for dynamic analysis. However, the model cannot be applied to the proposed machine since the model requires more than two stator windings. In the proposed model, the SPWM is reconstructed from a d-q equivalent circuit of the three-phase wound-rotor machine. It includes the dynamic characteristics of the machine. Besides, the vector control based on the model is considered by applying an isolated inverter to the rotor side. The speed and grid power factor can be simultaneously controlled through the inverter while the rotor power is regulated. Simulation and experimental results present the validity of the proposed model and control.