In order to reduce the total harmonic distortion (THD) of the grid-connected current caused by the high-frequency switching of the inverter, this paper combines the high efficiency single-phase H6-type inverter with LCL filter. The double closed-loop control method that consists of grid-connected current outer loop and capacitor current inner loop is put forward, by which a resonance peak of a low damping LCL filter is eliminated. In the grid-connected current outer loop, quasi proportion resonant (QPR) controller is adopted to overcome the steady-state error and weak anti-jamming capability in traditional PI controller. Finally, a simulation model is built in SIMULINK to verify the research. The simulation results show that, based on the single-phase H6-type inverter and LCL filter, the double closed-loop QPR control strategy can achieve the static error free tracking control of grid-connected current, which makes the system more stable and reduces the THD of grid-connected current effectively.