Flexible DC power grid can realize large-scale renewable energy wide-area coordinated complementarity and reliable transmission, and is an important development direction for high-voltage large-capacity flexible DC power transmission in the future. DC line short-circuit current is one of the important basis for selecting critical equipment parameters such as converter valves, DC circuit breakers and reactors in flexible DC grid. In this paper, a DC discharge equivalent circuit mathematical model considering AC infeed is established, and an analytical method is proposed to analyze the influence of the injected power of the converter station on the DC fault current. On this basis, the equivalent circuit model of the four-terminal bipolar flexible DC power grid is established based on the actual engineering, and the sensitivity analysis method is proposed to evaluate the influence of the DC power flow fluctuation on the fault current of the DC line. Finally, the validity and accuracy of the method are verified by PSCAD simulation. The method proposed in this paper can provide the necessary basis and reference for the equipment selection of flexible DC power grid.