This paper presents the theoretical analysis of the inherent reason of current harmonic and power oscillation phenomena in case of operating the microgrid inverter under unbalanced grid voltage conditions. In order to flexibly control the current harmonic and power oscillation, a new stationary frame control strategy is proposed. It has a simple control structure due to no need of a phase-locked loop and voltage/current positive/negative sequence extraction calculation. The coordinate control of power and current quality is achieved, which enhances the operation performance of microgrid inverter. Finally, the performance evaluation tests are carried out under unbalanced grid voltage conditions. Results verify the effectiveness of the propose method.