The multi-terminal flexible DC system offers high efficiency and economic benefits, making it particularly suitable for large-scale integration of renewable energy from multiple sites. However, compared to AC systems, DC systems have lower inertia and are more susceptible to disturbances, which can lead to system instability in severe cases. To address this issue, this paper proposes two inertia control methods: the inertia control method based on the equivalent sub-module number of the modular multilevel converter （MMC） and the inertia control method using virtual energy storage elements. The first method increases the equivalent capacitance of the MMC DC side by adjusting the number of sub-modules contributed by the upper and lower arms during the modulation process of the MMC. The second method introduces virtual energy storage on the MMC DC side by adding disturbance compensation to the outer loop power control. Building upon these approaches, this paper presents an inertia integrated control strategy for multi-terminal flexible DC systems, achieving better disturbance suppression by combining both control methods. Finally, a three-terminal flexible DC system model based on Nan’Ao Three-Terminal MTDC System is developed in PSCAD/EMTDC to validate the effectiveness of the proposed control strategy. The results show that, compared to systems without any inertia control strategy or those employing a single inertia control method, the system with the proposed inertia control strategy demonstrates the best suppression of DC voltage and active power fluctuations following a disturbance.