A single-phase grid-connected converter is considered in this paper in the presence of harmonic problems introduced non-linear loads. In order to compensate the harmonics caused by the loads, a local voltage support scheme is proposed. This is an added feature because its implementation is in parallel with a conventional current control method. Distinctively, the measurements of the grid or load current are not needed since the scheme is based on only local measurements. On top of a fundamental part for desired power injection, the converter output current comprises a harmonic part for compensation. Thus, the grid current harmonic distortion is minimized and the enhancement of the local voltage quality is achieved. A comprehensive model analysis indicates that the proposed strategy can help to attenuate harmonics of the local voltage without compromising on the quality of the fundamental current injection. Experimental results validate the effectiveness of the proposed control scheme. Moreover, the impact of grid frequency estimation error on the control strategy’s performance is quantified theoretically and experimentally.