<p>Conventional AC voltage sensorless predictive current control methods for grid-tied inverter are often sensitive to current DC offset errors, resulting in worse control performance. To solve this problem, this paper proposed an improved grid voltage observer as well as a new lumped DC offset observation method. First, the drawbacks of the conventional grid voltage observer are reviewed. Then, based on the backstepping design approach, an improved grid voltage observer is designed, which can remove the influences of the current DC offsets. Third, the effects of the current DC offset on the current control is analyzed, and a new lumped DC offset observation method is designed, which can estimate and compensate the current DC offset well. Fourth, based on the two proposed observers, a new AC voltage sensorless predictive current control method is achieved with enhanced robustness against current DC offset. Finally, experimental studies are carried out, which verify the strong robustness against current DC offsets of the proposed method.</p>