This paper proposes a generalized voltage droop (GVD) control strategy for control and power sharing in voltage source converter (VSC)-based multi-terminal DC (MTDC) grids. In the proposed approach, the conventional voltage droop characteristics of voltage-regulating VSC stations are replaced by the GVD characteristics. 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 proper adjustment of the GVD characteristics of the voltage-regulating converters. The proposed strategy improves the control and power-sharing capabilities of the conventional voltage droop, and enhances its maneuverability. Simulation results, obtained by detailed modeling in a four-terminal high voltage DC grid demonstrated the efficacy of the proposed approach and its flexibility in active power sharing. Moreover, based on the obtained results, switching between operating mode of the GVD control approach does not results in oscillations of the active powers flowing inside the MTDC grids.