The occurrence of asymmetric faults in the power grid will affect the reliable operation of the new energy grid-connected system, and there will be a risk of shutdown in severe cases. Given this, this paper proposes a voltage support strategy considering the degree of voltage sag under asymmetric faults. First, according to the output features of the inverter under asymmetric faults, the support principle of the point of common coupling (PCC) voltage is analyzed. Then the general formula of the PCC voltage amplitude under any asymmetrical fault is deduced, and after that the critical point of changing the reactive current injection mode is analyzed. Finally, considering the peak value of the inverter output current and the used capacity as constraints, three typical asymmetric faults are analyzed on the above groundwork. The optimal reactive current of each type of fault in a variety of voltage sag stages is determined, and the calculation formula of current reference value in each voltage sag stage is deduced. The effectiveness and superiority of the proposed control strategy is verified by the simulation results. This work is supported by the National Natural Science Foundation of China (No. 51708194).