Grid impedance variation has the possibility of leading to voltage oscillation and control instability, which poses a serious problem to electric vehicle (EV) charger design. In response to this problem, this paper proposes a robust control approach that is capable of dealing with grid impedance variation and system uncertainties. The proposed dual-loop control strategy is composed of an outer-loop proportional–integral (PI) controller and an inner-loop robust state feedback controller with integral action. The benefits of control are maximized according to linear matrix inequality (LMI) techniques. This paper aims to address the effects of grid impedance variation by including the uncertainty model considering the potential varying parameters in the control design process. Additionally, the uncertainty model considers sixteen possible sets, which are described by variations in the four most important parameters: grid impedance, grid resistance, filter impedance, and filter resistance. Compared to PI control, this LMI-based robust control method provides significantly improved disturbance rejection, faster transient response, and greater resilience to parameter variations, ensuring a more reliable and efficient operation of the EV charger. This proposed single-stage AC/DC EV charger topology also offers higher efficiency, reduced component count, and lower cost compared to conventional double-stage designs, making it a more compact, reliable, and economically attractive solution for modern electric vehicle charging systems. The simulation results confirm that the designed control method maintains excellent charging performance under different grid impedance conditions with a unity power factor.