Single-stage single-phase onboard electric vehicle (EV) chargers are popular owing to their simple structure and high efficiency. However, their performance during grid connection is highly dependent on grid impedance characteristics. In a real-world scenario, it is hard to determine the exact value of grid impedance because it varies over time. This creates a challenge for a controller design that is based on a certain value of impedance. In this paper, a robust current controller is presented for a single-stage single-phase onboard EV charger, considering both L-filter and uncertain grid impedance characteristics. A state-space model of a single-stage single-phase onboard EV charger incorporating grid impedance uncertainty is developed. Based on the uncertain model, an LMI-based robust current controller is designed considering both filter and grid impedance uncertainties. The robust current controller is presented by considering an uncertain model represented by a polytopic model with sixteen vertex systems. An all-pass filter is used to generate an orthogonal signal for a dq-frame implementation. Simulation results are presented to prove the robust current controller’s performance and robustness during different grid impedance conditions.