The DC distribution network is a low-inertia system, which is very sensitive to load disturbance, system failure, and other factors. By adding virtual capacitance to the converter connected to the power supply, the virtual inertia of the DC power grid can be improved. Firstly, this paper proposes a strategy for adjusting virtual capacitance based on the voltage change rate to achieve adaptive control of virtual inertia, which enables the converter to quickly absorb or release energy during power fluctuations. Secondly, the adaptivity of the strategy is improved and the main control parameters in the proposed control method are qualitatively analyzed. Finally, the four-terminal photovoltaic storage DC distribution network system is constructed. Through Simulink, the adaptive virtual inertia control is incorporated on the battery side to simulate and validate the effectiveness of the strategy and the rationality of parameter analysis. The results show that this method can provide flexible and adjustable inertia support for DC grids and improve the voltage stability of DC grids.