This paper proposes a generalized voltage droop (GVD) control strategy for dc voltage control and power sharing in voltage source converter (VSC)-based multiterminal dc (MTDC) grids. The proposed GVD control is implemented at the primary level of a two-layer hierarchical control structure of the MTDC grid, and constitutes an alternative to the conventional voltage droop characteristics of voltage-regulating VSC stations, providing higher flexibility and, thus, controllability to these networks. As a difference with other methods, the proposed GVD control strategy can be operated in three different control modes, including conventional voltage droop control, fixed active power control, and fixed dc voltage control, by adjusting the GVD characteristics of the voltage-regulating converters. Such adjustment is carried out in the secondary layer of the hierarchical control structure. The proposed strategy improves the control and power-sharing capabilities of the conventional voltage droop, and enhances its maneuverability. The simulation results, obtained by employing a CIGRE B4 dc grid test system, demonstrate the efficiency of the proposed approach and its flexibility in active power sharing and power control as well as voltage control. In these analysis, it will be also shown how the transitions between the operating modes of the GVD control does not give rise to active power oscillations in the MTDC grids.