In this paper, the delay problem of a deadbeat current control for a single-phase PWM inverter connected to the grid is investigated by applying z-transform. First, the effect of delay during one sampling period is discussed and then a predictive current observer-based controller is considered. The main objective of the control system is that the current has minimum harmonic distortion, and is in phase with the grid voltage. The control system has fast dynamic response when distortion occurs, and is robust against drift in the system parameters; it also places all the system closed-loop poles at the origin of the z-plane. Hence, it can achieve fast dynamic response with low total harmonic distortion, even under nonlinear loads. The simulation results are performed to verify the feasibility of the proposed control strategy.