The high-voltage multi-terminal dc (MTDC) systems are foreseen to experience an important development in the next years. Currently, they have appeared to be a prevailing technical and economical solution for harvesting offshore wind energy. In this study, inertia mimicry capability is added to a voltage-source converter-HVDC grid-side station in an MTDC grid connected to a weak ac grid, which can have low inertia or even operate as an islanded grid. The presented inertia mimicry control is integrated in the generalised voltage droop strategy implemented at the primary level of a two-layer hierarchical control structure of the MTDC grid to provide higher flexibility, and thus controllability to the network. Besides, complete control framework from the operational point of view is developed to integrate the low-level control of the converter stations in the supervisory control centre of the MTDC grid. A scaled laboratory test results considering the international council on large electric systems (CIGRE) B4 MTDC grid demonstrate the good performance of the converter station when it is connected to a weak islanded ac grid.