Environmental conditions and operational modes may significantly impact the distortion level of the injected current from single-phase grid-connected inverter systems, such as photovoltaic (PV) inverters, which may operate in cloudy days with a maximum power point tracking, in a non-unity power factor, or in the low voltage ride through mode with reactive current injection. In this paper, the mechanism of the harmonic current injection from grid-connected single-phase inverter systems is thus explored, and the analysis is conducted on single-phase PV systems. In particular, the analysis is focused on the impacts of the power factor and the feed-in grid current level on the quality of the feed-in grid current from single-phase inverters. As a consequence, an internal model principle based high performance current control solution is tailor-made and developed for single-phase grid-connected systems to produce high quality currents in different operation conditions, where a design procedure is also provided. The developed current controller in this paper can achieve a minimum steady-state error while maintaining a relatively fast transient response, and also being feasible in other single-phase applications as a promising harmonic mitigation solution. Experiments on single-phase grid-connected systems have verified the correctness of the relevant analysis and also the effectiveness of the tailor-made control solution in terms of good harmonic mitigation.