In the last decade, predictive current control (PCC) has been widely implemented for grid-connected voltage source inverters (VSIs) due to the advantages of low-current harmonic injection, fast dynamic response, and easy implementation for digital control systems. However, with the increasing switching frequency of VSIs applied to pursue a better output quality, inevitable time delays and uncertain system disturbances are aggravating system performance and stability, which presents a serious challenge for the PCC design. Thus, a new PCC algorithm has been proposed in this paper for a single-phase VSI to improve the quality of the current fed to the grid, as well as enhance the system stability and robustness. The proposed control scheme is developed from the traditional predictive current controller along with a simple weighted filter predictor and a robust adaptive voltage compensator. The results of simulation and experiment investigation have demonstrated the improvements of the proposed control scheme in inverter output quality and robustness to parameter variations.