Abstract: Accurate analysis of transient features of voltages and currents for flexible DC grids after DC faults is the theoretical basis of fault protection scheme design. The existing fault characteristic analysis methods using the initial traveling wave fail to effectively reflect the influence of the fault point on multiple refractions and reflections of fault traveling waves, which will produce large errors in case of a close-in fault. Using the established fault equivalent circuit of the flexible DC grid, the initial fault voltage at the fault point, the refraction and reflection coefficients at different positions, and the line-mode and ground-mode coupling coefficient at the fault point are acquired. A calculation method of the equivalent fault voltage at the fault point is proposed considering multiple refractions and reflection of the traveling wave. The numerical expressions of the transient voltages and currents can be obtained with the transfer functions of the fault voltages and currents at different positions. To simulate the fault, a ring topology four-terminal flexible DC grid simulation model is built in PSCAD/EMTDC. The correctness of the theoretical derivation is verified by comparing the simulation value with the theoretical calculation value.