For a grid-connected inverter in distributed generation systems, the current control is essential, and recently, the predictive current control based on a high performance digital signal processors (DSP) to satisfy a fast dynamic response has been widely investigated. However, the performance of predictive current control is degraded by the time delay due to digital implementation, the parameter and measured value errors and the interference of noise, and also theses make system even unstable. Therefore, this paper proposes the predictive current control using grid voltage observer for grid-connected inverter applications. To determine the relevant voltage observer gain, the low-order harmonics of grid voltage are considered, and the effect of filter parameter errors is analyzed. The proposed method has a fast current response capability, the robustness to noise and simple implementation due to voltage sensorless control and the robust current control performance to low-order grid harmonics. The feasibility of the proposed method is verified by simulation and experimental results.