This paper focuses on the droop-based dc voltage control design for multiterminal VSC-HVDC grid systems, considering the ac and the dc system dynamics. The droop control design relies on detailed linearized models of the complete multiterminal grid, including the different system dynamics, such as the dc grid, the ac grid, the ac connection filters, and the converter inner controllers. Based on the derived linear models, classical and modern control techniques are applied to design the different controllers, including a multivariable frequency analysis to design the grid voltage droop control. In combination with the droop control, a dc oscillation damping scheme is proposed in order to improve system performance. The control design is validated through simulations of a three-terminal system.