In order to improve the phenomenon that a traditional phase-locked loop based on a double second-order generalized integrator (DSOGI-PLL) cannot track signal amplitude and phase accurately when the input signal contains DC components and high-order harmonics, the structure of a second-order generalized integrator-quadrature signals generator (SOGI-QSG) is modified. The paper establishes the impedance model considering the DSOGI-PLL structure of the inductor-capacitor-inductor-type (LCL-type) inverter grid-connected system adopting current control measured from the grid terminal in alternating current side, introducing voltage feedback control to enhance the stability of the system. Meanwhile, analyzing the influence of parameters on impedance according to the impedance model established preferable design parameters. The improvement in SOGI-QSG structure is good for PLL to lock the grid voltage phase more accurately and the retrofitting in control strategy based on the impedance is able to uplift the inverter output impedance phase which is conducive to system stability by increasing the phase margin of the system. The simulation in Matlab/Simulink is carried out to verify the effectiveness of the proposed control strategy.