This paper proposes the control method for compensating for unbalanced grid current and reducing a total harmonic distortion (THD) of the grid current at the three-phase grid-connected inverter systems under unbalancd and distorted grid voltage conditions. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for a minimum point of THD. Both the gain and angle of a compensation voltage at the minimum point of THD of the grid current are derived. The negative-sequence components in the three-phase unbalanced grid voltage are cancelled in order to achieve the balanced grid current. The simulation and experimental results show the validity of the proposed control methods.