Due to the benefits of achieving low cost, light weight, and high performance, transformer-less inverters are frequently employed in grid-tied solar photovoltaic (PV) generation systems. However, additional steps must be taken to prevent security issues including ground fault currents and leakage currents, which can be prevented by connecting the PV panel to the ground through a parasitic capacitor. The proposal for new topologies with their control techniques and the modulation schemes have been inspired by the reduction of leakage currents issues. In this paper, improved topologies of single-phase transformerless inverter are proposed to reduce the leakage current and total harmonic distortion (THD) of grid current. These new topologies are named as H9 and H10 inverters according to the number of the switching devices in the inverter. Pulse width modulation (PWM) method is used for the inverters to suppress harmonics at the output grid current. The proposed H9 and H10 topologies can reduce the THD to 1.62% and 2.09%, respectively, at the grid current. The proposed topologies are extensively tested using simulation and test outcomes are presented.