The construction of new power system requires Hybrid Microgrids (HMG) to have inertia support capability, the application of Virtual Synchronous Generator (VSG) technology makes the sub-grids present different inertia characteristics, and the interlinking converter (ILC) makes the electrical characteristics of AC and DC buses coupled with each other during load fluctuation, resulting in ILC transmission power oscillation, which affects the dynamic stability of the system, therefore, the ILC transient power compensation is proposed to take into account the difference in inertia of sub-grids. During load fluctuation, the interlinking converter (ILC) couples the electrical characteristics of the AC and DC buses, which leads to the oscillation of the ILC transmission power and affects the dynamic stability of the system, therefore, the transient power compensation control of the ILC that takes into account the inertia difference of the sub-networks is proposed. A normalized equivalent VSG model of the AC-DC subnetwork is established to evaluate the equivalent inertia level of the subnetwork. The subnetwork equivalent inertia is further introduced into the transient power compensation controller to inject transient compensation power into the ILC to suppress the oscillation of the transmitted power and reduce the risk of overrun of the bus electrical quantity change rate. A simulation model is built based on the Matlab/Simulink platform, and the effectiveness of the proposed control strategy is verified under various operating conditions. Compared with the existing control strategy, the proposed control strategy can realize the overall power coordination and load sharing of the system, the drop of the AC/DC bus electric quantity change rate is mitigated, the ILC transmission power is smoother, and the dynamic performance of the system is improved.