In order to solve the problem that the voltage source converter based multi-terminal direct current (VSC-MTDC) system cannot provide inertia and participate in frequency modulation after connecting to the AC power grid under the traditional control strategy, an adaptive control strategy based on virtual inertia is proposed. First, the relationship between AC frequency and DC voltage was established by a virtual inertia control, allowing the VSC-MTDC system to provide inertia to the AC side. Second, to address the limited inertia coefficient selection due to DC voltage deviation, an adaptive control was adopted. When the DC voltage deviation is small, the inertia coefficient is increased to obtain a better inertial response; on the contrary, the inertia coefficient is reduced to prevent the DC voltage from exceeding the limit. Finally, to solve the problem of insufficient flexibility of the fixed droop coefficient, this paper introduces the power margin of a VSC-station into the droop coefficient to dynamically adjust the distribution ratio of unbalanced power and reduce the DC voltage deviation. The three-terminal VSC-MTDC system was modelled on the PSCAD/EMTDC simulation platform, and the superiority of the control strategy was highlighted in this paper by comparing it with conventional droop control and a fixed virtual inertia coefficient.