In this study, a coordinated voltage control strategy based on model predictive control (MPC) is proposed for offshore radial DC-connected wind farms. Two control modes are designed in this strategy. In the economic operation mode, the wind farm controller generates optimal active power references as well as bus voltage references of medium-voltage collector for DC-connected wind turbine (DCWT) systems and high-voltage DC/DC converters, where the goal is to minimize power losses inside the wind farm and ensure that voltages are within a feasible range, all while tracking the power references. In the voltage control mode, the main control objective for the wind farm controller is to minimize voltage deviations from the rated voltage. With the MPC, the control objective and operation constraints can be explicitly represented in the optimization problem while considering the dynamic response of the DCWT system. In addition, a sensitivity coefficient calculation method for radial DC-connected wind farms is developed to improve computational efficiency. Finally, DC-connected wind farms with 20 wind turbines are used to demonstrate the performance of the proposed strategy.