This paper proposes a novel control strategy in multi-terminal DC (MTDC) grids with offshore wind generation based on the idea of generalized voltage droop (GVD). In the proposed strategy, the GVD characteristics are assigned to the voltage-regulating converter station, enhancing their control maneuverability and enabling them to perform necessary DC voltage control and power sharing tasks. By adjusting the coefficients of the corresponding GVD characteristic, a converter station can be operated in three operating modes, namely (1) fixed active power control mode, (2) conventional voltage droop control mode or (3) fixed DC voltage control mode. Results of simulations on a test four-terminal DC grid including two offshore wind farm and two AC grids show the capabilities of the proposed control strategy. Moreover, simulation results confirmed stable operation of the GVD control in transition from one operating mode to another.