In view of the serious distortion of the output current of the inverter and the oscillation of the active and reactive power of the virtual synchronous generator (VSG) under the unbalanced power grid voltage, the proportion integral plus reduced order resonant (PI ROR) controller is used to improve the traditional VSG control strategy under the unbalanced voltage. PI ROR controller can realize the no difference control of negative sequence component without the separation calculation of positive and negative sequences of current and voltage, so it can put the positive sequence and negative sequence currents on the same dq axis for unified control. Compared with the traditional positive and negative sequences controller, it not only reduces the complexity of current loop control structure, but also avoids the control delay caused by a large number of positive and negative separation calculation. Finally, the simulation results show that the PI ROR controller can improve the steady and transient state performance of VSG under unbalanced voltage condition when cosidering the three control objectives of constant active power, constant reactive power and current balance.