There is a problem that the inertia of DC microgrid is low and it is easy for the voltage of a DC bus to be affected by power fluctuation in the network. Thus an adaptive virtual inertia control strategy based on improved model prediction for grid-connected converter of DC microgrid is proposed. First, adaptive analog virtual synchronous generator control is introduced into the voltage outer loop and, by combining the inertial parameters with the voltage change rate, flexible adjustment of the inertial parameters is realized. Secondly, model predictive control is applied in the current inner loop, along with an improved delay compensation algorithm, to achieve fast tracking of the desired current value and enhance the dynamic characteristics of the control system. Finally, a system model is established based on Matlab/Simulink for simulation. The results show that, compared with the traditional virtual inertia control strategy, the DC bus voltage fluctuation amplitude of the proposed control strategy is smaller and the dynamic performance is better. This can effectively improve the stability of the DC bus voltage and the inertia of the DC microgrid.