Grounding fault analysis is of vital importance for low voltage direct current (LVDC) supply and utilization systems. However, the existing DC grounding fault model is inappropriate for LVDC supply and utilization system. In order to provide an appropriate assessment model for the DC grounding fault impact on the LVDC supply and utilization system, an LVDC supply and utilization system grounding fault model is proposed in this paper. Firstly, the model is derived by utilizing capacitor current and voltage as the system state variable, which considers the impact of the converter switch state on the topology of the fault circuit. The variation of system state parameters under various fault conditions can be easily obtained by inputting system state data in normal conditions as the initial value. Then, a model solution algorithm for the proposed model is utilized to calculated the maximum fault current, the system maximum fault current with different grounding resistance is simple to acquired based on the solution algorithm. The calculation results demonstrate that grounding resistance and structure of LVDC supply and utilization system have remarkable impacts on the transient current. The effectiveness of the proposed model is verified in PSCAD/EMTDC. The simulation results indicate that the proposed method is appropriate for the system fault analysis under various fault conditions with different grounding resistance and the proposed model can offer theoretical guidance for system fault protection.