In this paper, a voltage droop control tuning strategy for a four-terminal high-voltage direct current (HVDC) grid is described, considering the DC multi-terminal grid, the AC grid and the modular multilevel converter (MMC) dynamics. A linear state-space model for such a system is derived including the different converter controllers. Based on this model, the primary DC grid droop voltage control design is addressed, highlighting the effect of the MMC dynamics. Finally, simulation results that validate the control design are obtained