Power grid occurs unbalanced grid voltage, In order to suppress the power fluctuations and high level of current harmonic distortion rate, proposes a control strategy of grid-connected inverter with LCL filter based on quasi proportional resonant in static coordinates. Firstly, in order to suppress the active power fluctuation, grid- given current is deduced by using instantaneous power theory. The positive and negative sequence power grid voltage acquisition method is presented. Using high efficiency filter characteristic of the LCL filter ,then established the grid-connection model based on active damping with QPR regulator in αβ static coordinates .The last simulation model is founded based on the MATLAB/SIMULINK .The simulation results show the control system can eliminate the active power oscillations and achieve low level of current harmonic distortion rate and verity the effectiveness of the proposed strategy.