Single-phase non-isolated inverters are widely utilized in distributed photovoltaic grid-connected applications. However, single-phase full-bridge inverters often suffer from the leakage current and the double-frequency power oscillation. A single-phase non-isolated inverter is investigated in this paper, which can handle the problem of the leakage current and the double-frequency power oscillation simultaneously. The presented inverter allows the neutral line of the AC grid directly connected to the negative terminal of the PV panel so that the leakage current is completely eliminated. Besides, based on a power decoupling method, the double-frequency power oscillation on the DC side can be suppressed without additional passive components. The state space model of the inverter is established and the influence of each parameter on its stability is analyzed in detail, and then an improved control strategy is proposed to reduce the inductance of the internal inductor. The effectiveness of the improved control strategy is verified by simulation and experimental results.