Under asymmetric voltage sag, distributed generation faces problems such as lack of coordination of multiple control objectives and high complexity of control strategies. These can lead to disconnection in serious cases and affect the stable operation of the power grid. Thus, a multi-objective active control strategy for DG is proposed considering voltage sags. First, the influence of grid impedance on voltage is fully considered, and the positive and negative sequence voltage supporting equation under asymmetric voltage sag is established to realize flexible control of phase voltage. Second, several control targets under asymmetric voltage sag based on positive and negative sequence active power and reactive current are established. The mutual restraint mechanism of multiple control objectives is analyzed, and the control objectives are optimized according to the voltage sag scenarios, and the objective function and constraint conditions in different scenarios are constructed. Finally, the Fmincon optimization algorithm is used to realize multi-objective optimal control of a grid-connected inverter under asymmetric voltage sag. Matlab/Simulink is used to verify the effectiveness of the proposed method in different voltage sag scenarios. This work is supported by the National Natural Science Foundation of China (No. 61873159).