The grid voltage, especially under unbalanced and harmonically distorted grid conditions, often distorts the injected currents of grid-connected inverters. To address this problem, a robust control scheme of grid-connected inverters is presented in this paper. The proposed scheme is achieved by an internal model (IM)-based current controller and a robust phase-locked loop (PLL) scheme. The robust PLL scheme employs open-loop filtering technique to offer exact steady-state performance as well as fast transient response. The IM-based current controller is stabilized using the linear matrix inequality approach to optimize the feedback gains, and implemented in the synchronous reference frame to reduce computational efforts. A state estimator is also introduced into current controller for the purpose of reducing the number of current sensors, which are often required in state feedback controller to damp the unstable dynamics of LCL filters. The validity of the proposed control scheme is demonstrated through comparative simulations and experimental results using a prototype grid-connected inverter.