To improve the operation performance of the PV inverter under the unbalanced grid voltage condition, a multi-objective coordinated control strategy based on the αβ coordinate is proposed in this paper. Firstly, the relationship between the output power and current under unbalanced grid voltage condition is deeply analyzed. It is pointed out that the contradiction between controlling the grid connected power constant and keeping low distortion rate output current. To deal with this problem, a control strategy based on weighted allocation of grid connected power instructions is proposed. Then, in order to realize the aforementioned control strategy, a repetitive controller is designed to track the output current. Finally, a simulation model based on PSCAD is used to validate the effectiveness of the proposed strategy.