The effective control of grid-connected inverters under complicated network situation is very important for the practical value. A dual-closed-loop control strategy based on grid-side current closed-loop and capacitor current closed-loop is proposed. Compared to conventional PI controller, it can ensure the system's speed, stability, unity power factor operation and good robustness during grid faults. Capacitor current inner-loop feedback control can suppress the LCL filter resonance peak, grid current outer-loop control based on stationary coordinate system needs no current decoupling, and the control algorithm is simple, quasi-proportional-resonant (QPR) has limited gain at the fundamental frequency, won’t cause system instability, and is capable to resist the grid frequency fluctuations. The advantages of this control strategy is analyzed, and effectiveness is validated by simulation.