Single-phase grid-connected converters are nowadays normally adopted in low-power and domestic applications. In order to improve the efficiency, while keeping the total cost of the system low, the converters are usually designed without an insulation transformer. Recently, these converters have witnessed an increased interest due to the widespread diffusion of renewable energy sources. In order to ensure the compliance with the international regulation for the grid connection, the Total Harmonic Distortion (THD) of the grid current must be maintained below specific thresholds indicated by the standards. For this reason, LCL filters allow to obtain a greater harmonic attenuation than a simple inductive filter. This paper proposes a deadbeat current control, specifically tailored for this application, which can ensure optimal reference tracking, rejection of the grid voltage disturbance and low computational effort. Simulation and experimental results show the effectiveness of the proposed solution.