This paper presents a coordinated voltage control scheme (CVCS) for a cluster of offshore wind power plants connected to a voltage-source converter-based high-voltage direct current system. The primary control point of the proposed voltage control scheme is the introduced Pilot bus, which is having the highest short-circuit capacity in the offshore AC grid. The developed CVCS comprehends an optimization algorithm, aiming for minimum active power losses in the offshore grid, to generate voltage reference to the Pilot bus. During the steady-state operation, the Pilot bus voltage is controlled by dispatching reactive power references to each wind turbine (WT) in the wind power plant cluster based on their available reactive power margin and network sensitivity-based participation factors, which are derived from the dV/dQ sensitivity of a WT bus w.r.t. the Pilot bus. This method leads to the minimization of the risk of undesired effects, particularly overvoltage at the terminals of the WT located far away from the AC collector substation, by dispatching lower reactive power references compared with the ones nearer to the substation. In addition, this paper proposes a control strategy for improved voltage ride through capability of WTs for faults in the offshore grid, thus leading to improved dynamic voltage profile in the offshore AC grid.