The fault characteristics of direct current (DC) grids can be analyzed by addressing the grid damping characteristics. However,the frequency-dependent characteristics of the transmission line parameters are usually ignored in the conventional grid impedance modeling methods,which cannot accurately reflect the grid damping characteristics. To compare and analyze the fault currents characteristics of the DC grids with cables and overhead lines,an impedance model of DC grid considering the frequency-dependent characteristics of the transmission line parameters based on vector fitting is proposed in this paper. Then,the proposed model is applied to compare and analyze the fault current features including time delays,initial rising rates and amplitudes of the DC grids with cables and overhead lines. Meanwhile,the impacts of the DC grids key parameters on the fault current characteristics of the two DC grids are investigated. Compared with the sweeping results of the frequency-dependent line model,the proposed model performs well in reflecting the damping characteristic of the DC grid,where the root square error is less than 0.6,informing that the proposed model is much more accurate than the simplified model. Finally,the simulation is conducted in a symmetrical monopolar two-terminal DC grid with pole-to-pole fault. The simulation results show that the fault current rising rate of the DC grid with cables is 24.96% higher than that of the DC grid with overhead lines when the arm inductance is increased,which validates that the fault currents of the DC grids with cables are more sensitive to the inductive key parameters than the DC grids with overhead lines.