A new multi-terminal DC (MTDC) grid controller based on model predictive control (MPC) for coordinating all droop controllers is proposed. This grid controller is designed to minimize the deviations of the DC voltages of the MTDC grid and avoid control mode change, so that to preserve the ability of droop voltage source converters (VSC) in controlling DC voltages. This is achieved by coordinately adjusting the gains of all droop controllers when changes in the MTDC grid power flow occur. A systematic discrete-time linear model of MTDC grid for this grid controller is derived in detail. In addition, the limitations on over shoot of DC voltages, converter capacity, and droop gain rate of change are taken into account in the MPC. Note that the constant droop gain will lead to a constant ratio $\Delta P/\Delta {U_{dc}}$ . Minimize the $\Delta {U_{dc}}$ means $\Delta P$ is minimized. So if necessary, the active power of a particular droop VSC can be fixed at a constant level by setting the lower and upper constraint on the corresponding droop gain to be equal. Tests are conducted on the system with six-terminal converters. The performance of the proposed grid controller is compared with those of fixed droop scheme. Simulation results have demonstrated the superiority and flexibility of the proposed grid controller under various operating conditions.