PI control can rapidly track the gridconnected current, however, the harmonic components of current are high due to the power electronic device of the inverter. In addition, PI parameters are difficult to adjust in practical application, and it is difficult to achieve optimization in the regulation process, which exacerbates the distortion of grid connected current. To achieve the best possible performance, an improved genetic algorithm is considered to optimize parameters of PI control. By calculating the error of practical current with setting current, this algorithm builds the current fitness function. The optimal PI parameters are obtained by iterating remarkably and the distortion rate is reduced. The combination of repetitive control technique significantly improves the steady performance by building the specific frequency notch filter and second order low pass filter. Through Matlab/Simulink, a model of gridconnected inverter with LC filter is built and the performances of the three control strategies of PI control, PI repetitive control and improved genetic PI repetitive control are compared to verify the effectiveness of proposed control strategy.