This paper proposes a single-phase grid-connected wound rotor machine that has the single-phase stator and three-phase rotor windings. The machine has no auxiliary winding or capacitor unlike conventional single-phase machines. Nevertheless, it can operate in all four quadrants of the torque-speed plane with a three-phase inverter. For adjustable speed drives, an isolated three-phase inverter is applied to the rotor windings while the stator winding is directly connected to a single-phase source. The grid filter and rectifier of the conventional system are eliminated and the rotor-side slip rings can be also removed by the inverter integration. So the overall structure of the proposed drive system is simple and cost effective. In this paper, the proposed machine is modeled into a modified d-q model considering the absence of q-axis stator coil. Its characteristics are analyzed and vector control methods of the grid power factor, dc-link voltage, and speed are proposed. For more efficient control, the optimal rotor current set is calculated from the minimum copper loss condition. The system has wider operating areas than other single-phase drive systems. The feasibility of the proposed system is verified by experiments.